Analyse des données de nouvelles hospitalisations/réanimations/décès de la COVID-19

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Source de données utilisées:

• Données hospitalières relatives à l’épidémie de COVID-19 : https://www.data.gouv.fr/fr/datasets/donnees-hospitalieres-relatives-a-lepidemie-de-covid-19/

• Données relatives aux résultats des tests virologiques COVID-19 : https://www.data.gouv.fr/fr/datasets/donnees-relatives-aux-resultats-des-tests-virologiques-covid-19/

Questions de recherche:

• Peut-on expliquer le nombre de nouvelles entrées par semaine en fonction du nombre de personnes testées positives quelques jours auparavant ?

• Peut-on expliquer les entrées en réanimation par les entrées en hospitalisations ?

• Peut-on expliquer les nouveaux décès par les entrées réanimations ?

En fonction des réponses aux questions précédentes :

• Peut-on prédire à court terme les nouveaux cas positifs, les nouvelles hospitalisations, les nouvelles réanimations et les nouveaux décès ?

Packages et fonctions locales à charger:

library(cartogram)
library(cartography)

## Warning in fun(libname, pkgname): rgeos: versions of GEOS runtime 3.9.0-CAPI-1.16.2
## and GEOS at installation 3.8.0-CAPI-1.13.1differ

library(forecast)
library(kableExtra)
library(rgdal)
library(tidyverse)
library(vistime)
library(zoo)
source("fonctions.R")

Version de R utilisée:

R.version

##                _                           
## platform       x86_64-pc-linux-gnu         
## arch           x86_64                      
## os             linux-gnu                   
## system         x86_64, linux-gnu           
## status                                     
## major          4                           
## minor          0.3                         
## year           2020                        
## month          10                          
## day            10                          
## svn rev        79318                       
## language       R                           
## version.string R version 4.0.3 (2020-10-10)
## nickname       Bunny-Wunnies Freak Out

1 Données hospitalières relatives à l’épidémie de COVID-19

1.1 Présentation des données

1.1.1 Données par département

Dans un premier temps, on met à jour les données tous les jours de façon automatique.

# Date du jour pour actualiser les données:
to_day <- Sys.Date()
my_url <- "https://www.data.gouv.fr/fr/datasets/r/6fadff46-9efd-4c53-942a-54aca783c30c"
if (!file.exists(paste0(getwd(), "/data/", to_day, ".csv"))) {
    download.file(my_url, destfile = paste0(getwd(), "/data/", to_day, ".csv"))
}
hospital <- read.csv(paste0(getwd(), "/data/", to_day, ".csv"), sep = ";")
# On ajoute le nom des régions:
hospital <- merge(hospital, dep_region, by = "dep")
# On utilise le format date pour coder le jour:
hospital$jour <- as.Date(hospital$jour)

Comment se présente les données du Ministère de la Santé ?

temp <- hospital[hospital$dep == "69" & hospital$jour > to_day - 5, ]
kableExtra::kbl(temp)

	dep	jour	incid_hosp	incid_rea	incid_dc	incid_rad	nom_dep	region
24067	69	2021-02-24	59	7	10	38	Rhône	Auvergne-Rhône-Alpes
24073	69	2021-02-23	50	15	6	42	Rhône	Auvergne-Rhône-Alpes
24100	69	2021-02-25	53	15	11	45	Rhône	Auvergne-Rhône-Alpes
24121	69	2021-02-26	64	18	8	28	Rhône	Auvergne-Rhône-Alpes
24124	69	2021-02-22	54	17	14	21	Rhône	Auvergne-Rhône-Alpes

Ici il s’agit des données qui donnent chaque jour par département :

• le nombre de nouvelles entrées en hospitalisations
• le nombre de nouvelles entrées en réanimations
• le nombre de décés
• le nombre de sorties

On créé des fenêtres de 7 jour à partir du dernier jour observé. Par exemple si nous avons les données d’hospitalisation jusqu’au 25 février 2021 la semaine qui correspond à la semaine t0 correspond à la fenêtre [19 février 2021; 25 février 2021]. Dans chaque fenêtre, on calcule le nombre de nouvelles hospitalisations, réanimations et décès par département.

hospital$semaine <- num_semaine(hospital$jour)
# On aggrège les données en fonction de cette fenêtre et on garde tous les départements:
my_basis <- hospital %>%
  group_by(dep, semaine) %>%
  dplyr::summarize(hosp = sum(incid_hosp),
            rea = sum(incid_rea),
            rad = sum(incid_rad),
            dc = sum(incid_dc),
            jour = max(jour),
            region = unique(region))

timeline_data <- data.frame(event = c("Semaine t0", "Semaine t1", "Semaine t2", "Semaine t3"), 
                            start = c(to_day - 8, to_day - 15, to_day - 22, to_day - 29), 
                            end = c(to_day - 1, to_day - 8, to_day - 15, to_day - 22), group = "temps")
vistime(timeline_data)

1.1.2 Données par région

On dispose égaglement des données d’hospitalisations/réanimations/décès par classe d’âge à la différence qu’il s’agit de données régionales et qu’il s’agit des données de stock (nombre d’hospitalisations et réanimations en cours) et pas du nombre de nouvelles hospitalisations. On peut toutefois estimer le nombre de nouvelles hospitalisations ou décès en faisant les différences des valeurs d’un jour sur l’autre.

my_url <- "https://www.data.gouv.fr/fr/datasets/r/08c18e08-6780-452d-9b8c-ae244ad529b3"
if (!file.exists(paste0(getwd(), "/data/age", to_day, ".csv"))) {
  download.file(my_url, destfile = paste0(getwd(), "/data/age", to_day, ".csv"))
}
hospital_age <- read.csv(paste0(getwd(), "/data/age", to_day, ".csv"), sep = ";")
# On ajoute le nom des régions:
hospital_age <- merge(hospital_age, code_region, by.x = "reg", by.y = "code")
# On utilise le format date pour coder le jour:
hospital_age$jour <- as.Date(hospital_age$jour)
# on affecte la semaine
hospital_age$semaine <- num_semaine(hospital_age$jour)

# on calcule les nouvelles hospitalisations/réanimations/décès
hospital_age$new_hosp <- 0
hospital_age$new_rea <- 0
hospital_age$new_dc <- 0

for (k in nrow(hospital_age):1) {
  age_k <- hospital_age$cl_age90[k] 
  jour_k <- hospital_age$jour[k] 
  reg_k <- hospital_age$reg[k] 
  rad_k <- hospital_age$rad[k] 
  dc_k <- hospital_age$dc[k] 
  
  ind_k <- which(hospital_age$reg == reg_k & hospital_age$cl_age90 == age_k & hospital_age$jour == jour_k - 1)
  if (length(ind_k) == 1) {
    hospital_age$new_hosp[k] <- max((hospital_age$hosp[k] - hospital_age$hosp[ind_k]) + 
                                (hospital_age$dc[k] - hospital_age$dc[ind_k]) +     
                              (hospital_age$rad[k] - hospital_age$rad[ind_k]) +
                              (hospital_age$rea[k] - hospital_age$rea[ind_k]), 0)
    hospital_age$new_rea[k] <- max((hospital_age$dc[k] - hospital_age$dc[ind_k]) +     
                              (hospital_age$rea[k] - hospital_age$rea[ind_k]), 0) 
    hospital_age$new_dc[k] <- max((hospital_age$dc[k] - hospital_age$dc[ind_k]), 0) 
  }
}
# on aggrege par semaine
my_basis_age <- hospital_age %>%
  group_by(region, semaine, cl_age90) %>%
  dplyr::summarize(hosp = sum(new_hosp),
                   rea = sum(new_rea),
                   dc = sum(new_dc),
            jour = max(jour),
            region = unique(region))
# On met au format wide
my_basis_age_wide <- tidyr::pivot_wider(my_basis_age,
                           id_cols = c("semaine", "region", "jour", "hosp", "rea", "dc", "cl_age90"),
                           names_from = "cl_age90",
                           values_from = c("hosp", "rea", "dc"))

1.2 Quelle est la situation cette semaine ?

On va calculer quelques chiffres clés pour mesure la situation des régions sur les 7 derniers jours qui viennent de s’écouler : [19 février 2021; 25 février 2021].

# On aggrège les données par région sur la semaine `r paste0("[", format(to_day - 7, '%d %B %Y'), "; ",  format(to_day - 1, '%d %B %Y'), "]")` :
vs_my_basis_t0 <- my_basis %>%
  filter(semaine %in% "semaine_t00") %>%
  group_by(region) %>%
  summarise(hosp = sum(hosp),
            rea = sum(rea),
            dc = sum(dc)) 
# On aggrège les données par région sur la semaine `r paste0("[", format(to_day - 13, '%d %B %Y'), "; ",  format(to_day - 7, '%d %B %Y'), "]")` :
vs_my_basis_t1 <- my_basis %>%
  filter(semaine %in% "semaine_t01") %>%
  group_by(region) %>%
  summarise(hosp = sum(hosp),
            rea = sum(rea),
            dc = sum(dc)) 

1.2.1 Résumé des hospitalisations

On représente par région:

• le nombre total de nouvelles hospitalisations (semaine [19 février 2021; 25 février 2021]).

• le nombre moyen journalier de nouvelles hospitalisations (semaine [19 février 2021; 25 février 2021]).

• l’évolution (en pourcentage) entre la semaine [12 février 2021; 18 février 2021] et la semaine [19 février 2021; 25 février 2021].

hosp_region <- vs_my_basis_t0 %>%
  select(region, hosp) %>%
  mutate(`moyenne jour` = hosp / 7,
         `evolution en %` = (vs_my_basis_t0$hosp - vs_my_basis_t1$hosp) / vs_my_basis_t1$hosp * 100) %>%
    rename(`total semaine` = hosp) %>%
  arrange(-`total semaine`)
# On représente les données :
hosp_region[, 3] <- round(hosp_region[, 3])
hosp_region[, 4] <- round(hosp_region[, 4], 1)
hosp_region[2:4] <- lapply(hosp_region[2:4], function(x) {
    cell_spec(x, bold = T, color = spec_color(x, end = 0.9),
              font_size = spec_font_size(x))
})
hosp_region <- rbind(hosp_region, tibble(region = "France entière", 
          `total semaine` = sum(vs_my_basis_t0$hosp), 
          `moyenne jour` = round(sum(vs_my_basis_t0$hosp) / 7, 0), 
          `evolution en %` = round((sum(vs_my_basis_t0$hosp) - sum(vs_my_basis_t1$hosp)) / 
                                     sum(vs_my_basis_t1$hosp) * 100, 1)))
kbl(hosp_region, escape = F, align = "c") %>% kable_classic("striped", full_width = F)

region	total semaine	moyenne jour	evolution en %
Ile-de-France	2192	313	10.8
Provence-Alpes-Côte d’Azur	1370	196	-3.4
Hauts-de-France	1309	187	19.2
Auvergne-Rhône-Alpes	1133	162	-8.3
Grand Est	773	110	-8.1
Occitanie	547	78	6.2
Bourgogne-Franche-Comté	403	58	-18.4
Centre-Val de Loire	391	56	19.6
Nouvelle-Aquitaine	388	55	-14.9
Normandie	331	47	-18.9
Pays de la Loire	317	45	19.6
DOM-TOM	253	36	-1.2
Bretagne	228	33	-10.9
Corse	20	3	-70.1
France entière	9655	1379	0.4

On représente par département la carte des nouvelles hospitalisations sur la dernière semaine observée ([19 février 2021; 25 février 2021])

# On importe les contours des départements
dep.2015 <- readOGR(dsn="./departements 2015/DEPARTEMENT", layer="DEPARTEMENT")

## OGR data source with driver: ESRI Shapefile 
## Source: "/media/thibault/My Passport/confinement/covid/departements 2015/DEPARTEMENT", layer: "DEPARTEMENT"
## with 96 features
## It has 11 fields

dep.2015@data$CODE_DEPT <- as.character(dep.2015@data$CODE_DEPT) 

# data 
dep.2015_00 <- merge(dep.2015, filter(my_basis, semaine == "semaine_t00"), 
                     by.x = "CODE_DEPT", by.y = "dep")
# On représente les nouvelles hospitalisations sur la dernière semaine observée (`r paste0("[", format(to_day - 7, '%d %B %Y'), "; ",  format(to_day - 1, '%d %B %Y'), "]")`) (Source pour le code : https://rgeomatic.hypotheses.org/1361#more-1361)
# quantization breaks of the rate
bks <- c(0, getBreaks(v = dep.2015_00$hosp, method = "kmeans", nclass = 5))
# correct the breaks to use the global rate as limit of class 
# get a color palette
cols <- carto.pal(pal1 = "green.pal", n1 = 3, pal2 = "wine.pal", n2 = 3)
## Choropleth layer
# set figure margins and background color
par(mar = c(0, 0, 1.2, 0), bg = "lemonchiffon")
# Hospitalisations
choroLayer(spdf = dep.2015_00, var = "hosp", breaks = bks, col = cols,
           border = "khaki", lwd = 0.5, 
           legend.title.txt = "Hospitalisations", 
           legend.pos = 'topleft', legend.values.rnd = 0)
# add a title and layout
layoutLayer(title = paste0("Nouvelles hospitalisations ", 
  paste0("[", format(to_day - 7, '%d %B %Y'), "; ",  format(to_day - 1, '%d %B %Y'), "]")), 
            sources = "", north = TRUE, scale = 50, tabtitle = TRUE,
            theme = "sand.pal", frame = FALSE,  
            author = "")

1.2.2 Résumé des réanimations

On représente par région:

• le nombre total de nouvelles réanimations (semaine [19 février 2021; 25 février 2021]).

• le nombre moyen journalier de nouvelles réanimations (semaine [19 février 2021; 25 février 2021]).

• l’évolution (en pourcentage) entre la semaine [12 février 2021; 18 février 2021] et la semaine [19 février 2021; 25 février 2021].

rea_region <- vs_my_basis_t0 %>%
  select(region, rea) %>%
  mutate(`moyenne jour` = rea / 7,
         `evolution en %` = (vs_my_basis_t0$rea - vs_my_basis_t1$rea) / vs_my_basis_t1$rea * 100) %>%
    rename(`total semaine` = rea) %>%
  arrange(-`total semaine`)
# On représente les données :
rea_region[, 3] <- round(rea_region[, 3])
rea_region[, 4] <- round(rea_region[, 4], 1)
rea_region[2:4] <- lapply(rea_region[2:4], function(x) {
    cell_spec(x, bold = T, color = spec_color(x, end = 0.9),
              font_size = spec_font_size(x))
})

rea_region <- rbind(rea_region, tibble(region = "France entière", 
          `total semaine` = sum(vs_my_basis_t0$rea), 
          `moyenne jour` = round(sum(vs_my_basis_t0$rea) / 7, 0), 
          `evolution en %` = round((sum(vs_my_basis_t0$rea) - sum(vs_my_basis_t1$rea)) / 
                                     sum(vs_my_basis_t1$rea) * 100, 1)))

kbl(rea_region, escape = F, align = "c") %>% kable_classic("striped", full_width = F)

region	total semaine	moyenne jour	evolution en %
Ile-de-France	467	67	12.8
Hauts-de-France	254	36	10
Provence-Alpes-Côte d’Azur	253	36	4.1
Auvergne-Rhône-Alpes	235	34	-6.7
Grand Est	146	21	0.7
Occitanie	111	16	-14
Centre-Val de Loire	89	13	78
Nouvelle-Aquitaine	74	11	-5.1
Bourgogne-Franche-Comté	64	9	-17.9
DOM-TOM	64	9	12.3
Normandie	49	7	-18.3
Pays de la Loire	41	6	-10.9
Bretagne	27	4	8
Corse	4	1	-42.9
France entière	1878	268	3.5

On représente par département la carte des nouvelles réanimations sur la dernière semaine observée ([19 février 2021; 25 février 2021])

# quantization breaks of the rate
bks <- c(0, getBreaks(v = dep.2015_00$rea, method = "kmeans", nclass = 5))
# correct the breaks to use the global rate as limit of class 
# get a color palette
cols <- carto.pal(pal1 = "green.pal", n1 = 3, pal2 = "wine.pal", n2 = 3)
## Choropleth layer
# set figure margins and background color
par(mar = c(0, 0, 1.2, 0), bg = "lemonchiffon")
# Hospitalisations
choroLayer(spdf = dep.2015_00, var = "rea", breaks = bks, col = cols,
           border = "khaki", lwd = 0.5, 
           legend.title.txt = "Réanimations", 
           legend.pos = 'topleft', legend.values.rnd = 0)
# add a title and layout
layoutLayer(title = paste0("Nouvelles Réanimations ", 
  paste0("[", format(to_day - 7, '%d %B %Y'), "; ",  format(to_day - 1, '%d %B %Y'), "]")), 
            sources = "", north = TRUE, scale = 50, tabtitle = TRUE,
            theme = "sand.pal", frame = FALSE,  
            author = "")

1.2.3 Résumé des décès

On représente par région:

• le nombre total de nouveaux décès (semaine [19 février 2021; 25 février 2021]).

• le nombre moyen journalier de nouveaux décès (semaine [19 février 2021; 25 février 2021]).

• l’évolution (en pourcentage) entre la semaine [12 février 2021; 18 février 2021] et la semaine [19 février 2021; 25 février 2021].

dc_region <- vs_my_basis_t0 %>%
  select(region, dc) %>%
  mutate(`moyenne jour` = dc / 7,
         `evolution en %` = (vs_my_basis_t0$dc - vs_my_basis_t1$dc) / vs_my_basis_t1$dc * 100) %>%
    rename(`total semaine` = dc) %>%
  arrange(-`total semaine`)
# On représente les données :
dc_region[, 3] <- round(dc_region[, 3])
dc_region[, 4] <- round(dc_region[, 4], 1)
dc_region[2:4] <- lapply(dc_region[2:4], function(x) {
    cell_spec(x, bold = T, color = spec_color(x, end = 0.9),
              font_size = spec_font_size(x))
})

dc_region <- rbind(dc_region, tibble(region = "France entière", 
          `total semaine` = sum(vs_my_basis_t0$dc), 
          `moyenne jour` = round(sum(vs_my_basis_t0$dc) / 7, 0), 
          `evolution en %` = round((sum(vs_my_basis_t0$dc) - sum(vs_my_basis_t1$dc)) / 
                                     sum(vs_my_basis_t1$dc) * 100, 1)))

kbl(dc_region, escape = F, align = "c") %>% kable_classic("striped", full_width = F)

region	total semaine	moyenne jour	evolution en %
Ile-de-France	370	53	-2.1
Provence-Alpes-Côte d’Azur	250	36	-15.3
Auvergne-Rhône-Alpes	239	34	-5.9
Hauts-de-France	222	32	2.3
Grand Est	178	25	-11
Occitanie	105	15	-29.5
Nouvelle-Aquitaine	93	13	-21.2
Bourgogne-Franche-Comté	87	12	-16.3
Centre-Val de Loire	79	11	9.7
Normandie	65	9	-20.7
Bretagne	55	8	-11.3
Pays de la Loire	50	7	-29.6
DOM-TOM	22	3	-24.1
Corse	1	0	-90.9
France entière	1816	259	-11.1

On représente par département la carte des nouveaux décès sur la dernière semaine observée ([19 février 2021; 25 février 2021])

# quantization breaks of the rate
bks <- c(0, getBreaks(v = dep.2015_00$dc, method = "kmeans", nclass = 5))
# correct the breaks to use the global rate as limit of class 
# get a color palette
cols <- carto.pal(pal1 = "green.pal", n1 = 3, pal2 = "wine.pal", n2 = 3)
## Choropleth layer
# set figure margins and background color
par(mar = c(0, 0, 1.2, 0), bg = "lemonchiffon")
# Hospitalisations
choroLayer(spdf = dep.2015_00, var = "dc", breaks = bks, col = cols,
           border = "khaki", lwd = 0.5, 
           legend.title.txt = "Décès", 
           legend.pos = 'topleft', legend.values.rnd = 0)
# add a title and layout
layoutLayer(title = paste0("Nouveaux décès ", 
  paste0("[", format(to_day - 7, '%d %B %Y'), "; ",  format(to_day - 1, '%d %B %Y'), "]")), 
            sources = "", north = TRUE, scale = 50, tabtitle = TRUE,
            theme = "sand.pal", frame = FALSE,  
            author = "")

1.3 Comment a évolué la situation depuis le début de l’épidémie ?

1.3.1 Graphique d’évolution

1.3.1.1 Hospitalisations

Ici, on représente le nombre d’entrée en hospitalisations par semaine en fonction du temps sur la France entière.

my_basis_fr <- my_basis %>%
  group_by(semaine, jour) %>%
  summarise(hosp = sum(hosp),
            rea = sum(rea),
            dc = sum(dc))
p <- ggplot(data = my_basis_fr,
            aes(x = jour, y = hosp)) +
  geom_line() +
  labs(title = "Nouvelles hospitalisations par semaine",
       x = "semaine",
       y = "hospitalisations",
       fill = "Age") 
plotly::ggplotly(p)

On représente la même figure mais en mettant en relief la répartition des valeurs par région :

my_basis$region <- factor(my_basis$region, levels = hosp_region$region)
# On aggrège les données par région et semaine:
my_basis_by_region <- my_basis %>%
  group_by(semaine, region) %>%
  summarize(hosp = sum(hosp),
            rea = sum(rea),
            dc = sum(dc),
            jour = max(jour))
# On représente les shares par tranche d'age 
p <- ggplot(my_basis_by_region) + 
  aes(x = jour, y = hosp, fill = region) +
  geom_area(color = "black") +
  labs(title = "Nouvelles hospitalisations par région",
       x = "Semaine",
       y = "Total",
       fill = "Hospitalisation") +
  scale_fill_brewer(palette = "Set3") +
  theme_minimal() 
plotly::ggplotly(p)

On représente la même figure mais en mettant en relief la répartition des valeurs par classe d’âge :

# On aggrège les données par age et semaine:
my_basis_by_age_1 <- my_basis_age %>%
  group_by(semaine, cl_age90) %>%
  summarize(hosp = sum(hosp),
            rea = sum(rea),
            dc = sum(dc),
            jour = max(jour))
# On représente les shares par tranche d'age 
p <- ggplot(filter(my_basis_by_age_1, cl_age90 != 0)) + 
  aes(x = jour, y = hosp, fill = factor(cl_age90)) +
  geom_area(color = "black") +
  labs(title = "Nouvelles hospitalisations par classe d'âges",
       x = "Semaine",
       y = "Total",
       fill = "Hospitalisation") +
  scale_fill_brewer(palette = "Set3") +
  theme_minimal() 
plotly::ggplotly(p)

On met les valeurs en pourcentages pour que le graphique soit plus visible

# On aggrège les données par age et semaine:
my_basis_by_age_2 <- my_basis_age %>%
  filter(cl_age90 != 0) %>%
  group_by(semaine, cl_age90) %>%
  summarize(hosp = sum(hosp),
            rea = sum(rea),
            dc = sum(dc),
            jour = max(jour)) %>%
  group_by(cl_age90)  %>%
  group_by(semaine) %>%
  mutate(percent_hosp = hosp / sum(hosp),
         percent_rea = rea / sum(rea), 
         percent_dc = dc / sum(dc))
# On représente les shares par tranche d'age 
p <- ggplot(my_basis_by_age_2) + 
  aes(x = jour, y = percent_hosp, fill = factor(cl_age90)) +
  geom_area(color = "black") +
  labs(title = "Répartition des nouvelles hospitalisations par classe d'âges",
       x = "Semaine",
       y = "Total",
       fill = "Hospitalisation") +
  scale_fill_brewer(palette = "Set3") +
  theme_minimal() 
plotly::ggplotly(p)

1.3.1.2 Réanimations

On représente le nombre cummulé d’entrée en réanimations par semaine en fonction du temps sur la France entière.

p <- ggplot(data = my_basis_fr,
            aes(x = jour, y = rea)) +
  geom_line() +
  labs(title = "Nouvelles réanimations par semaine",
       x = "semaine",
       y = "réanimations",
       fill = "Age") 
plotly::ggplotly(p)

On représente la même figure mais en mettant en relief la répartition des valeurs par région :

# On représente les shares par régions
p <- ggplot(my_basis_by_region) + 
  aes(x = jour, y = rea, fill = region) +
  geom_area(color = "black") +
  labs(title = "Nouvelles réanimations par région",
       x = "Semaine",
       y = "Total",
       fill = "Réanimations") +
  scale_fill_brewer(palette = "Set3") +
  theme_minimal() 
plotly::ggplotly(p)

On représente la même figure mais en mettant en relief la répartition des valeurs par classe d’âge :

p <- ggplot(filter(my_basis_by_age_1, cl_age90 != 0)) + 
  aes(x = jour, y = rea, fill = factor(cl_age90)) +
  geom_area(color = "black") +
  labs(title = "Nouvelles réanimations par classe d'âges",
       x = "Semaine",
       y = "Total",
       fill = "Réanimations") +
  scale_fill_brewer(palette = "Set3") +
  theme_minimal() 
plotly::ggplotly(p)

On met les valeurs en pourcentages pour que le graphique soit plus visibles

# On représente les shares par tranche d'age 
p <- ggplot(my_basis_by_age_2) + 
  aes(x = jour, y = percent_rea, fill = factor(cl_age90)) +
  geom_area(color = "black") +
  labs(title = "Répartition des nouvelles réanimations par classe d'âges",
       x = "Semaine",
       y = "Total",
       fill = "Réanimations") +
  scale_fill_brewer(palette = "Set3") +
  theme_minimal() 
plotly::ggplotly(p)

Enfin, on représente le ratio réanimations / hospitalisations :

p <- ggplot(data = my_basis_by_age_2,
            aes(x = jour, y = rea / hosp, col = factor(cl_age90))) +
  geom_line() +
  labs(title = "Ratio réanimations/hospitalisations par semaine",
       x = "semaine",
       y = "Ratio réa / hospi",
       color = "Age") 
plotly::ggplotly(p)

1.3.1.3 Décès

On représente le nombre cummulé de nouveaux décès par semaine en fonction du temps sur la France entière.

p <- ggplot(data = my_basis_fr,
            aes(x = jour, y = dc)) +
  geom_line() +
  labs(title = "Nouveux décès par semaine",
       x = "semaine",
       y = "décès",
       fill = "Age") 
plotly::ggplotly(p)

On représente la même figure mais en mettant en relief la répartition des valeurs par région :

# On représente les shares par régions
p <- ggplot(my_basis_by_region) + 
  aes(x = jour, y = dc, fill = region) +
  geom_area(color = "black") +
  labs(title = "Nouveux décès par région",
       x = "Semaine",
       y = "Total",
       fill = "Décès") +
  scale_fill_brewer(palette = "Set3") +
  theme_minimal() 
plotly::ggplotly(p)

On représente la même figure mais en mettant en relief la répartition des valeurs par classe d’âge :

p <- ggplot(filter(my_basis_by_age_1, cl_age90 != 0)) + 
  aes(x = jour, y = dc, fill = factor(cl_age90)) +
  geom_area(color = "black") +
  labs(title = "Nouveux décès par classe d'âges",
       x = "Semaine",
       y = "Total",
       fill = "Décès") +
  scale_fill_brewer(palette = "Set3") +
  theme_minimal() 
plotly::ggplotly(p)

On met les valeurs en pourcentages pour que le graphique soit plus visibles

# On représente les shares par tranche d'age 
p <- ggplot(my_basis_by_age_2) + 
  aes(x = jour, y = percent_dc, fill = factor(cl_age90)) +
  geom_area(color = "black") +
  labs(title = "Répartition des nouveux décès par classe d'âges",
       x = "Semaine",
       y = "Total",
       fill = "Décès") +
  scale_fill_brewer(palette = "Set3") +
  theme_minimal() 
plotly::ggplotly(p)

Enfin, on représente le ratio décès / réanimations :

p <- ggplot(data = my_basis_by_age_2,
            aes(x = jour, y = dc / rea, col = factor(cl_age90))) +
  geom_line() +
  labs(title = "Ratio décès/réanimations par semaine",
       x = "semaine",
       y = "Ratio décès / réanimations",
       color = "Age") 
plotly::ggplotly(p)

1.3.2 Graphique d’évolution du nombre d’hospitalisations par départements groupés par région

On va s’intéresser au nombre d’hospitalisations. On peut représenter cette information département par département. Ici, on représente le nombre cummulé d’entrée par semaine en fonction du temps.

On représente d’abord les 4 régions actuellement les plus touchées et pour lesquelles l’axe des ordonnées va de 0 à 1200.

p <- ggplot(data = filter(my_basis, region %in% c("Provence-Alpes-Côte d'Azur",
                                                  "Auvergne-Rhône-Alpes", 
                                                  "Hauts-de-France",
                                                   "Ile-de-France")),
            aes(x = jour, y = hosp, color = region, group = dep)) +
  geom_line() + 
  coord_cartesian(ylim = c(0, 1200)) +
  facet_wrap(~ region, nrow = 4)
plotly::ggplotly(p)

On représente ensuite les 8 régions suivantes les plus touchées mais avec une échelle différente sur l’axe des ordonnées (0 à 400):

p <- ggplot(data = filter(my_basis, region %in% c("Occitanie",
                                                  "Grand Est", 
                                                  "Bourgogne-Franche-Comté",
                                                  "Nouvelle-Aquitaine", 
                                                  "Normandie",
                                                  "Pays de la Loire", 
                                                  "Centre-Val de Loire",
                                                  "Bretagne")),
            aes(x = jour, y = hosp, color = region, group = dep)) +
  geom_line()  + 
  coord_cartesian(ylim = c(0, 400)) +
  facet_wrap(~ region, nrow = 8)
plotly::ggplotly(p)

Enfin, on représente les 2 régions les moins touchées et avec une échelle différente sur l’axe des ordonnées (0 à 200):

p <- ggplot(data = filter(my_basis, region %in% c("DOM-TOM", "Corse")),
            aes(x = jour, y = hosp, color = region, group = dep)) +
  geom_line()  + 
  coord_cartesian(ylim = c(0, 200)) +
  facet_wrap(~ region, nrow = 2)
plotly::ggplotly(p)

1.3.3 Cartes d’évolution sur les 6 dernières semaines

On représente l’évolution des hospitalisations sur les 6 dernières semaines:

On représente l’évolution des réanimations sur les 6 dernières semaines:

On représente l’évolution des décès sur les 6 dernières semaines:

1.4 Départements avec les plus fortes évolutions en valeurs absolues par rapport à la semaine précédente

On calcule la différence entre le nombre de nouveaux patients hospitalisés sur la période [19 février 2021; 25 février 2021] et sur la période [11 février 2021; 18 février 2021]

my_basis_evol <- merge(my_basis %>% 
  filter(semaine == "semaine_t00") %>%
  rename(hosp_t0 = hosp) %>%
  select(dep, hosp_t0, region),
    my_basis %>% 
  filter(semaine == "semaine_t01") %>%
  select(dep, hosp) %>%
  rename(hosp_t1 = hosp),
by = "dep") %>%
  mutate(diff_abs = hosp_t0 - hosp_t1,
         diff_rel = (hosp_t0 - hosp_t1) / hosp_t1) %>%
  mutate(evol = factor(ifelse(diff_rel < 0, "<0", 
                       ifelse(diff_rel >= 0 & diff_rel < 0.5, "[0,50%[",
                           ifelse(diff_rel >= 0.5 & diff_rel < 1, "[50,100%[", 
                                  ifelse(diff_rel >= 1 & diff_rel < 2, "[100,200%[",
                                         ">200%")))), 
                       levels = c("<0", "[0,50%[", "[50,100%[", "[100,200%[", ">200%")))
my_basis_evol_long <- tidyr::pivot_longer(data = my_basis_evol,
                                   col = c(2, 4),
                                   names_to = "semaine",
                                   values_to = "hospitalisations")
my_basis_evol_long$semaine <- factor(my_basis_evol_long$semaine,
      levels = c("hosp_t1", "hosp_t0"),
      labels = c(paste0("[", format(to_day - 14, '%d %b'), "; ",  
                        format(to_day - 8, '%d %b'), "]"),
                 paste0("[", format(to_day - 7, '%d %b'), "; ",  
                        format(to_day - 1, '%d %b'), "]")))

On va représenter des couleurs différentes en fonction du taux d’évolution découpées en 5 classes

• taux d’évolution négatif
• taux compris entre 0 et \(50\%\)
• taux compris entre \(50\%\) et \(100\%\)
• taux compris entre \(100\%\) et \(200\%\)
• taux supérieur à \(200\%\)

p <- ggplot(my_basis_evol_long, aes(x = semaine, y = hospitalisations, colour = evol, group = dep))+
    geom_line() +
  scale_colour_manual(values = c("blue", "#FC9272", "#FB6A4A", "#DE2D26", "#A50F15")) + 
  facet_wrap(~region)
plotly::ggplotly(p)

2 Données relatives aux résultats des tests virologiques COVID-19

On met à jour les données chaque jour :

# On récupére directement l'url depuis le site du ministère:
url <- "https://www.data.gouv.fr/fr/datasets/r/406c6a23-e283-4300-9484-54e78c8ae675"
if (!file.exists(paste0(getwd(), "/data/test", to_day, ".csv"))) {
  download.file(url, destfile = paste0(getwd(), "/data/test", to_day, ".csv"))
    }
test <- read.csv(paste0(getwd(), "/data/test", to_day, ".csv"), sep = ";")
# on enlève les départements qui ne sont pas présents dans la table hopital
test <- test %>%
  filter(!(dep %in% c("975", "977", "978")))
# On utilise le format date pour coder le jour:
test$jour <- as.Date(test$jour)
test$semaine <- num_semaine(test$jour, begin = max(hospital$jour) - 3, decallage = TRUE)
test_region <- merge(test, dep_region, by = "dep")

On va calculer quelques chiffres clés pour mesurer la situation des régions sur une fenêtre de 7 jours [16 février 2021; 22 février 2021]. On ne peut pas représenter les 7 derniers jours car les données ne sont pas encore diffusées.

# On aggrège les données par région sur la semaine `r paste0("[", format(to_day - 7, '%d %B %Y'), "; ",  format(to_day - 1, '%d %B %Y'), "]")` :
vs_my_basis_t0 <- test_region %>%
  filter(semaine %in% "semaine_t0-1", cl_age90 == 0) %>%
  group_by(region) %>%
  summarise(P = sum(P)) 
# On aggrège les données par région sur la semaine `r paste0("[", format(to_day - 13, '%d %B %Y'), "; ",  format(to_day - 7, '%d %B %Y'), "]")` :
vs_my_basis_t1 <- test_region %>%
  filter(semaine %in% "semaine_t00", cl_age90 == 0) %>%
  group_by(region) %>%
  summarise(P = sum(P)) 

On représente par région:

• le nombre total de testés positifs (semaine [16 février 2021; 22 février 2021]).

• le nombre moyen journalier de testés positifs (semaine [16 février 2021; 22 février 2021]).

• l’évolution (en pourcentage) entre la semaine [09 février 2021; 15 février 2021] et la semaine [16 février 2021; 22 février 2021].

P_region <- vs_my_basis_t0 %>%
  select(region, P) %>%
  mutate(`moyenne jour` = P / 7,
         `evolution en %` = (vs_my_basis_t0$P - vs_my_basis_t1$P) / vs_my_basis_t1$P * 100) %>%
    rename(`total semaine` = P) %>%
  arrange(-`total semaine`)
# On représente les données :
P_region[, 3] <- round(P_region[, 3])
P_region[, 4] <- round(P_region[, 4], 1)
P_region[2:4] <- lapply(P_region[2:4], function(x) {
    cell_spec(x, bold = T, color = spec_color(x, end = 0.9),
              font_size = spec_font_size(x))
})
P_region <- rbind(P_region, tibble(region = "France entière", 
          `total semaine` = sum(vs_my_basis_t0$P), 
          `moyenne jour` = round(sum(vs_my_basis_t0$P) / 7, 0), 
          `evolution en %` = round((sum(vs_my_basis_t0$P) - sum(vs_my_basis_t1$P)) / 
                                     sum(vs_my_basis_t1$P) * 100, 1)))
kbl(P_region, escape = F, align = "c") %>% kable_classic("striped", full_width = F)

region	total semaine	moyenne jour	evolution en %
Ile-de-France	31452	4493	4.3
Hauts-de-France	16201	2314	4.8
Provence-Alpes-Côte d’Azur	15728	2247	-14.2
Auvergne-Rhône-Alpes	12654	1808	-12.5
Grand Est	8490	1213	-12.1
Occitanie	7572	1082	-21.1
Nouvelle-Aquitaine	5934	848	-7.4
Pays de la Loire	4798	685	4.8
Normandie	4403	629	-2.4
Bourgogne-Franche-Comté	3732	533	-13.8
Centre-Val de Loire	3571	510	-7.5
Bretagne	3045	435	0.7
DOM-TOM	2853	408	-18.7
Corse	384	55	15.3
France entière	120817	17260	-5.8

2.1 Représentation des testés positifs par tranche d’âge en fonction du temps

On représente les testés positifs par tranche d’age:

# On aggrège les données par tranche d'age et semaine:
test_by_age <- test %>%
  filter(cl_age90 != 0) %>%
  group_by(semaine, cl_age90) %>%
  summarize(P = sum(P),
            jour = max(jour)) %>%
  group_by(semaine) %>%
  mutate(percent_P = P / sum(P))
p <- ggplot(test_by_age) + 
  aes(x = jour, y = P, fill = factor(cl_age90)) +
  geom_area(color = "black") +
  labs(title = "Nombre de téstés positifs par classe d'âge ",
       x = "Week",
       y = "Effectifs",
       fill = "Age") +
  scale_fill_brewer(palette = "Set3") +
  theme_minimal() 
plotly::ggplotly(p)

On représente les testés positifs par région :

test_region$region <- factor(test_region$region, levels = hosp_region$region)
test_by_region <- test_region %>%
  filter(cl_age90 == 0) %>%
  group_by(semaine, region) %>%
  summarize(P = sum(P),
            jour = max(jour)) %>%
  group_by(semaine) %>%
  mutate(percent_P = P / sum(P))
p <- ggplot(test_by_region) + 
  aes(x = jour, y = P, fill = factor(region)) +
  geom_area(color = "black") +
  labs(title = "Nombre de testés positifs par région",
       x = "Week",
       y = "Effectifs",
       fill = "Region") +
  scale_fill_brewer(palette = "Set3") +
  theme_minimal() 
plotly::ggplotly(p)

2.2 Graphique d’évolution du nombre de détectés positifs par départements groupés par région

test_by_dep <- test_region %>%
  filter(cl_age90 == 0) %>%
  group_by(semaine, region, dep) %>%
  summarize(P = sum(P),
            jour = max(jour)) %>%
  group_by(semaine) %>%
  mutate(percent_P = P / sum(P))

p <- ggplot(data = test_by_dep, 
            aes(x = jour, y = P, color = region, group = dep)) +
  geom_line() +
  coord_cartesian(ylim = c(0, 20000)) +
  facet_wrap(~ region)
plotly::ggplotly(p)

2.3 Choix du décallage

Hypothèse: on suppose que le nombre d’admis en hospitalisations à la semaine t0 dépend du nombre de cas testés positifs sur une fenêtre de 7 jours qui aura commencé 10 jours avant la semaine t0. Exemple: la semaine t0 est [19 février 2021; 25 février 2021], on va l’expliquer par le nombre de personnes testées positive du [09 février 2021; 15 février 2021].

3 Préparation des données pour la modélisation

On prépare ici les données pour l’étape de modélisation:

# On aggrège les données par département et semaine:
test_by <- test %>%
  filter(cl_age90 != 0) %>%
  group_by(dep, semaine, cl_age90) %>%
  summarize(P = sum(P),
            jour = max(jour)) %>%
  group_by(dep, semaine) %>%
  mutate(percent_P = P / sum(P))
# On passe d'un format long à un format wide les tranches d'âge pour les avoir comme des variables explicatives
test_by$cl_age90 <- paste0("tranche_", test_by$cl_age90)
test_long <- tidyr::pivot_wider(test_by,
                           id_cols = c("semaine", "dep", "jour", "P", "cl_age90"),
                           names_from = "cl_age90",
                           values_from = "P")
# On aggrège les données par département et semaine:
test_by <- test_long %>%
  group_by(dep, semaine) %>%
  summarize(tranche_9 = sum(tranche_9),
            tranche_19 = sum(tranche_19),
            tranche_29 = sum(tranche_29),
            tranche_39 = sum(tranche_39),
            tranche_49 = sum(tranche_49),
            tranche_59 = sum(tranche_59),
            tranche_69 = sum(tranche_69),
            tranche_79 = sum(tranche_79),
            tranche_89 = sum(tranche_89),
            tranche_90 = sum(tranche_90)) %>%
  mutate(tranche_0 = tranche_9 + tranche_19 + tranche_29 + tranche_39 + 
           tranche_49 + tranche_59 + tranche_69 + tranche_79 + tranche_89 + tranche_90)

# On merge les jeux de données :
my_basis <- merge(my_basis, test_by, by = c("dep", "semaine"), all.y = T)
my_basis[which(is.na(my_basis$jour)), "jour"] <- to_day + 6
my_basis[which(is.na(my_basis$region)), "region"] <- dep_region$region[match(my_basis[which(is.na(my_basis$region)), "dep"], dep_region$dep)]

3.1 Représentation du lien entre entre le nombre d’hospitalisations et le nombre de testés positifs

Dans un premier temps, on va rerésenter les départements par des cercles de taille proportionnelle aux nombres de testés positifs la semaine du [09 février 2021; 15 février 2021]. La couleur dépend du nombre d’hospitalisations observés la semaine du [19 février 2021; 25 février 2021].

dep.2015_00 <- merge(dep.2015, filter(my_basis, semaine == "semaine_t00"), 
                     by.x = "CODE_DEPT", by.y = "dep")
w <- 1 - (dep.2015_00$tranche_0 / max(dep.2015_00$tranche_0)) 
dep.2015_dorling <- cartogram_dorling(dep.2015_00, "tranche_0", m_weight = w, k = 5)
# dep.2015$tranche_0 <- as.numeric(dep.2015$tranche_0)
# dep.2015_ncont <- cartogram_ncont(dep.2015, "tranche_0")
# set figure margins and background color
par(mar = c(0, 0, 1.2, 0), bg = "lemonchiffon")
# Hospitalisations
bks <- c(0, getBreaks(v = dep.2015_00$hosp, method = "kmeans", nclass = 5))
# correct the breaks to use the global rate as limit of class 
# get a color palette
cols <- carto.pal(pal1 = "green.pal", n1 = 3, pal2 = "wine.pal", n2 = 3)
choroLayer(spdf = dep.2015_dorling, var = "hosp", breaks = bks, col = cols, lwd = 0.5,
           legend.title.txt = "Hospitalisations", 
           legend.pos = 'topleft', legend.values.rnd = 0)
# plot(dep.2015, add = T, border = "khaki")
# add a title and layout
layoutLayer(title = paste0("Nouvelles hospitalisations ", 
  paste0("[", format(to_day - 7, '%d %B %Y'), "; ",  format(to_day - 1, '%d %B %Y'), "]")), 
            sources = "", north = TRUE, scale = 50, tabtitle = TRUE,
            theme = "sand.pal", frame = FALSE,  
            author = "")

On représente le nombre de nouvelles hospitalisations par semaine et par département en fonction du nombre de personnes testées positives quelques jours auparavant et on constate un lien très fort.

p <- ggplot(my_basis) +                
  aes(x = tranche_0, y = hosp) +     
  geom_point() +                  
  geom_smooth(method = "loess") + 
  geom_smooth(method = "lm",     
              col = "red") +
  facet_wrap(~ region)
plotly::ggplotly(p)

4 Prédire le nombre de testés positifs

On rappelle que les données sur le nombre de testés positifs ne sont disponible que jusqu’au 22 février 2021. Notre objectif est de prédire le nombre de testés positifs du 23 février 2021 au 01 mars 2021 en utilisant des modèles de séries temporelles. En utilisant un modèle de série temporelle on suppose que ce qu’on observe à la date \(j\) dépend de ce qu’il s’est passé les dates antérieures. On va utiliser 3 modèles différents et en fonction de leur performence (sur les données passées), on va leur donner plus ou moins d’importance.

4.1 Modèle de type Box-Jenkins

Ici, on considère les données journalières, et non hebdomadaires. On va expliquer \(y_{d, t}^a\), le nombre de testés positifs le jour \(t\) dans le département \(d\) et dans la tranche d’âge \(a\). La stratégie utilisée est la suivante :

• on différencie chaque série pour les rendre stationnaire (on ne vérifiera pas l’hypothèse de stationarité après la différenciation car on modélise énormément de modèle, ici on a \(A\times D\) séries où \(A\) est le nombre de classe d’âge et \(D\) le nombre de département et notre but est d’avoir une procédure automatique)

• on cherche le meilleur modèle \(ARIMA(p,d,q)\) selon le critère AIC, à l’aide de la fonction auto.arima() (package forecast)

• on prédit sur les 7 prochains jours à venir et on cummule ces prédictions pour avoir une prédiction du nombre de cas positifs sur la semaine à venir.

4.2 Modèle de type Lissage exponentiel

On va appliquer deux modèles de lissage exponentiels:

• un modèle journalier qui va permettre de modéliser \(y_{d, t}^a\), le nombre de testés positifs le jour \(t\) dans le département \(d\) et dans la tranche d’âge \(a\) afin de prédire le nombre de testés positifs dans les 7 jours.

• un modèle hebdomadaire qui va permettre de modéliser \(y_{d, s}^a\), le nombre de testés positifs la semaine \(s\) dans le département \(d\) et dans la tranche d’âge \(a\) afin de prédire le nombre de testés positifs la semaine à venir.

4.3 Combinaison des prédictions

On apprentit les modèles ci-dessus en enlevant la dernière semaine observée dans le but de donner des poids différents aux trois modèles de prédictions utilisés. Ainsi, on donnera davantage de poids aux modèles qui ont mieux prédit la dernière semaine observée.

# prediction par department 
nom_dep <- my_basis[my_basis$semaine == "semaine_t00", "dep"]
pred_cas <- numeric(length(nom_dep))
my_tab <- data.frame(true_P = numeric(0), pred_1 = numeric(0), pred_2 = numeric(0), pred_3 = numeric(0))
      
# apprentissage
for (k in length(nom_dep):1) {
  if (nom_dep[k] %in% c("975", "977", "978")) {
    my_basis <- rbind(data_k, my_basis)
  } else {
    for (age in c(0, 9, 19, 29, 39, 49, 59, 69, 79, 89, 90)) {
      
      # apprentissage
      temp <- test[test$dep == nom_dep[k] & test$cl_age90 == age & test$jour <= max(test$jour) - 7, ]
      my_ts <- zoo(temp$P, temp$jour)
      
      # Methode 1 : ARIMA
      my_ts_diff <- diff(my_ts)
      # tseries::adf.test(my_ts) 
      # tseries::adf.test(my_ts_diff)
      my_mod <- forecast::auto.arima(my_ts_diff)
      forecast_my_mod <- as.numeric(forecast(my_mod)$mean)
      pred_1 <- round(sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:7]), 0)
      # Méthode 2 : lissage exponentiel
      my_mod_exp <- ets(my_ts)
      forecast_my_mod_exp <- as.numeric(forecast(my_mod_exp)$mean)
      forecast_my_mod_exp <- ifelse(forecast_my_mod_exp > 0, forecast_my_mod_exp, 0)
      pred_2 <- round(sum(forecast_my_mod_exp[1:7]), 0)
      # Méthode 3 : lissage exponentiel sur données hebdomadaires
      temp <- my_basis[my_basis$dep == nom_dep[k] & !(my_basis$semaine %in% c("semaine_t0-1", "semaine_t0-2")), ]
      my_ts_exp <- zoo(temp[ , paste0("tranche_", age)], temp$jour)
      my_mod_exp_2 <- ets(my_ts_exp)
      forecast_my_mod_exp <- as.numeric(forecast(my_mod_exp_2)$mean)
      forecast_my_mod_exp <- ifelse(forecast_my_mod_exp > 0, forecast_my_mod_exp, 0)
      pred_3 <- round(forecast_my_mod_exp[1], 0)
      
      true_P <- sum(test[which(test$dep == nom_dep[k] & test$cl_age90 == age & 
                               test$jour > (max(test$jour) - 7)), "P"])
      my_tab <- rbind(my_tab, data.frame(true_P = true_P, pred_1 = pred_1, pred_2 = pred_2, pred_3 = pred_3))
    }
  }
}

res_lm_cas <- lm(true_P ~ pred_1 + pred_2 + pred_3, data = my_tab)

for (k in length(nom_dep):1) {
  data_k <- data.frame(dep = nom_dep[k], semaine = "semaine_t0-2", hosp = NA, rea = NA, rad = NA, dc = NA,
                         jour = to_day + 13, region = dep_region[match(nom_dep[k], dep_region$dep) , "region"],
                         tranche_9 = NA, tranche_19 = NA,  tranche_29 = NA,  tranche_39 = NA,  tranche_49 = NA, 
                         tranche_59 = NA,  tranche_69 = NA,  tranche_79 = NA,  tranche_89 = NA,  tranche_90 = NA, 
                         tranche_0  = NA)
  data_k_2 <- data.frame(dep = nom_dep[k], semaine = "semaine_t0-2", hosp = NA, rea = NA, rad = NA, dc = NA,
                         jour = to_day + 13, region = dep_region[match(nom_dep[k], dep_region$dep) , "region"],
                         tranche_9 = NA, tranche_19 = NA,  tranche_29 = NA,  tranche_39 = NA,  tranche_49 = NA, 
                         tranche_59 = NA,  tranche_69 = NA,  tranche_79 = NA,  tranche_89 = NA,  tranche_90 = NA, 
                         tranche_0  = NA)
      
  if (nom_dep[k] %in% c("975", "977", "978")) {
    my_basis <- rbind(data_k, my_basis)
  } else {
    for (age in c(0, 9, 19, 29, 39, 49, 59, 69, 79, 89, 90)) {
      # modèle journaliers 
      temp <- test[test$dep == nom_dep[k] & test$cl_age90 == age, ]
      my_ts <- zoo(temp$P, temp$jour)
      my_ts_diff <- diff(my_ts)
      # tseries::adf.test(my_ts) 
      # tseries::adf.test(my_ts_diff)
      my_mod <- forecast::auto.arima(my_ts_diff)
      forecast_my_mod <- as.numeric(forecast(my_mod)$mean)
      pred_1 <- round(sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:7]), 0)
      # modèles exponentiels
      # Méthode 2 : lissage exponentiel
      my_mod_exp <- ets(my_ts)
      forecast_my_mod_exp <- as.numeric(forecast(my_mod_exp)$mean)
      forecast_my_mod_exp <- ifelse(forecast_my_mod_exp > 0, forecast_my_mod_exp, 0)
      pred_2 <- round(sum(forecast_my_mod_exp[1:7]), 0)
      # Méthode 3 : lissage exponentiel sur données hebdomadaires
      temp <- my_basis[my_basis$dep == nom_dep[k] & !(my_basis$semaine %in% c("semaine_t0-2")), ]
      my_ts_exp <- zoo(temp[ , paste0("tranche_", age)], temp$jour)
      my_mod_exp_2 <- ets(my_ts_exp)
      forecast_my_mod_exp <- as.numeric(forecast(my_mod_exp_2)$mean)
      forecast_my_mod_exp <- ifelse(forecast_my_mod_exp > 0, forecast_my_mod_exp, 0)
      pred_3 <- round(forecast_my_mod_exp[1], 0)
      data_k[ , paste0("tranche_", age)] <- predict(res_lm_cas, newdata = data.frame(pred_1 = pred_1,
                                                                                     pred_2 = pred_2,
                                                                                     pred_3 = pred_3))
    }
    my_basis <- rbind(data_k, my_basis)
  }
}

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

## Warning in ets(my_ts_exp): Missing values encountered. Using longest contiguous
## portion of time series

On représente les testés positifs par région en ajoutant les valeurs de la semaine prédite:

test_by_region <- my_basis %>%
  group_by(semaine, region) %>%
  summarize(P = sum(tranche_0),
            jour = max(jour)) 
test_by_region$region <- factor(test_by_region$region, levels = hosp_region$region)
p <- ggplot(test_by_region) + 
  aes(x = jour - 10, y = P, fill = factor(region)) +
  geom_area(color = "black") +
  labs(title = "Prédictions du nombre de testés positifs par région",
       x = "Week",
       y = "Effectifs",
       fill = "Region") +
  scale_fill_brewer(palette = "Set3") +
  theme_minimal() 
plotly::ggplotly(p)

On aggrège les données à la France entière:

  my_basis_fr <- my_basis %>%
    group_by(semaine, jour) %>%
    summarise(P = sum(tranche_0))
  p <- ggplot(data = filter(my_basis_fr, semaine %in% c("semaine_t0-2", "semaine_t0-1", "semaine_t00")),
              aes(x = jour - 10, y = P)) +
    geom_line(col = "red") +
    geom_line(data = filter(my_basis_fr, !(semaine %in% c("semaine_t0-2"))), 
              aes(x = jour - 10, y = P)) +
  labs(title = "Prédiction des nouveaux cas positifs dans les 7 jours",
       x = "semaine",
       y = "Cas positifs",
       fill = "Age") 
plotly::ggplotly(p)

5 Prédire le nombre d’hospitalisation de la semaine à venir

5.1 Modèle linéaire 1 (sur les départements) en fonction du nombre de cas détectés positifs : 1 modèle par région

Ici, pour chaque région \(r\), le modèle est de la forme

\[y_{i,t}^r=\beta_0^r+\beta_1^rx_{i,t'}^r+\epsilon_{i,t}^r\] avec:

• \(y_{i,t}\) le nombre d’entrées à l’hôpital dans le département \(i\in r\) sur la période \(t\), où \(t\) est une fenêtre de 7 jours.
• \(x_{i,t'}\) est le nombre de testés positifs dans le département \(i\in r\) sur la période \(t'\) où \(t'\) correspond à la fenêtre \(t\), décalé de 10 jours.

En d’autres termes, on fait ici un modèle de régression par région. Cela suppose que le lien entre les tests virologiques et le nombre d’hospitalisation est homogène à l’intérieur d’une région et peut différer d’une région à une autre.

Apprentissage:

On modélise sur les observations des semaines précédentes:

res_lm <- lm(hosp ~  region + tranche_0:region - 1, 
             data = my_basis[!(my_basis$semaine %in% c("semaine_t0-2", "semaine_t0-1", "semaine_t00")), ])

stargazer::stargazer(res_lm, type = "html")

	Dependent variable:
	hosp
regionAuvergne-Rhône-Alpes	14.706***
	(1.736)
regionBourgogne-Franche-Comté	10.309***
	(2.289)
regionBretagne	4.318
	(3.356)
regionCentre-Val de Loire	8.690***
	(2.734)
regionCorse	1.991
	(4.653)
regionDOM-TOM	0.672
	(3.056)
regionGrand Est	12.856***
	(2.040)
regionHauts-de-France	28.832***
	(2.711)
regionIle-de-France	30.469***
	(2.619)
regionNormandie	6.242**
	(2.895)
regionNouvelle-Aquitaine	3.039*
	(1.829)
regionOccitanie	3.553**
	(1.691)
regionPays de la Loire	14.307***
	(2.981)
regionProvence-Alpes-Côte d’Azur	7.932***
	(2.577)
regionAuvergne-Rhône-Alpes:tranche_0	0.063***
	(0.001)
regionBourgogne-Franche-Comté:tranche_0	0.074***
	(0.003)
regionBretagne:tranche_0	0.058***
	(0.004)
regionCentre-Val de Loire:tranche_0	0.058***
	(0.004)
regionCorse:tranche_0	0.043*
	(0.024)
regionDOM-TOM:tranche_0	0.100***
	(0.007)
regionGrand Est:tranche_0	0.069***
	(0.002)
regionHauts-de-France:tranche_0	0.055***
	(0.001)
regionIle-de-France:tranche_0	0.057***
	(0.001)
regionNormandie:tranche_0	0.071***
	(0.003)
regionNouvelle-Aquitaine:tranche_0	0.061***
	(0.003)
regionOccitanie:tranche_0	0.053***
	(0.002)
regionPays de la Loire:tranche_0	0.048***
	(0.003)
regionProvence-Alpes-Côte d’Azur:tranche_0	0.084***
	(0.001)
Observations	3,939
R2	0.926
Adjusted R2	0.926
Residual Std. Error	32.943 (df = 3911)
F Statistic	1,750.776*** (df = 28; 3911)
Note:	p<0.1; p<0.05; p<0.01

On représente comme si on on avait fait un modèle par région pour faciliter la lecture des coefficients :

stargazer::stargazer(res_lm_r1, res_lm_r2, res_lm_r3, res_lm_r4, res_lm_r5, res_lm_r6, res_lm_r7, 
                     res_lm_r8, res_lm_r9, res_lm_r10, res_lm_r11, res_lm_r12, res_lm_r13, res_lm_r14, 
                     type = "html", column.labels = nom_region)

	Dependent variable:
	hosp
	Auvergne-Rhône-Alpes	Hauts-de-France	Provence-Alpes-Côte d’Azur	Grand Est	Occitanie	Normandie	Nouvelle-Aquitaine	Centre-Val de Loire	Bourgogne-Franche-Comté	Bretagne	Corse	Pays de la Loire	Ile-de-France	DOM-TOM
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)
tranche_0	0.063***	0.055***	0.084***	0.069***	0.053***	0.071***	0.061***	0.058***	0.074***	0.058***	0.043***	0.048***	0.057***	0.100***
	(0.001)	(0.001)	(0.002)	(0.002)	(0.001)	(0.002)	(0.001)	(0.002)	(0.003)	(0.003)	(0.005)	(0.002)	(0.001)	(0.005)
Constant	14.706***	28.832***	7.932*	12.856***	3.553***	6.242***	3.039***	8.690***	10.309***	4.318**	1.991*	14.307***	30.469***	0.672
	(2.183)	(4.644)	(4.473)	(1.900)	(0.813)	(2.314)	(0.933)	(1.523)	(2.165)	(1.961)	(1.048)	(2.211)	(3.697)	(1.978)
Observations	468	195	234	390	507	195	468	234	312	156	78	195	312	195
R2	0.913	0.891	0.906	0.809	0.894	0.845	0.830	0.742	0.728	0.769	0.460	0.732	0.881	0.710
Adjusted R2	0.913	0.890	0.906	0.809	0.894	0.844	0.829	0.741	0.727	0.767	0.453	0.731	0.881	0.708
Residual Std. Error	41.432 (df = 466)	56.436 (df = 193)	57.170 (df = 232)	30.685 (df = 388)	15.841 (df = 505)	26.338 (df = 193)	16.808 (df = 466)	18.352 (df = 232)	31.155 (df = 310)	19.256 (df = 154)	7.422 (df = 76)	24.441 (df = 193)	46.504 (df = 310)	21.325 (df = 193)
F Statistic	4,912.146*** (df = 1; 466)	1,573.525*** (df = 1; 193)	2,235.673*** (df = 1; 232)	1,644.387*** (df = 1; 388)	4,272.981*** (df = 1; 505)	1,054.538*** (df = 1; 193)	2,268.156*** (df = 1; 466)	666.076*** (df = 1; 232)	829.206*** (df = 1; 310)	512.232*** (df = 1; 154)	64.857*** (df = 1; 76)	527.158*** (df = 1; 193)	2,298.509*** (df = 1; 310)	472.225*** (df = 1; 193)
Note:	p<0.1; p<0.05; p<0.01

Test:

On teste le modèle sur les données de la semaine actuelle:

pred_1 <- predict(res_lm, newdata = my_basis[my_basis$semaine == "semaine_t00", ])

plot(pred_1, my_basis[my_basis$semaine == "semaine_t00", "hosp"],
     xlab = "valeurs prédites", ylab = "valeurs observées")
abline(a = 0, b = 1)
text(pred_1, my_basis[my_basis$semaine == "semaine_t00", "hosp"], 
     my_basis[my_basis$semaine == "semaine_t00", "dep"], pos = 2)

L’écart quadratique moyen est égal ici à :

mean((pred_1 - my_basis[my_basis$semaine == "semaine_t00", "hosp"]) ^ 2, na.rm = T)

## [1] 1737.9

5.2 Modèle linéaire 2 (sur les région) : 1 modèle par classe d’âge

Ici, on va faire un modèle qui prend en compte les classes d’âges. Les données d’hospitalisation par classe d’âge ne sont disponibles que par région. Le modèle est de la forme

\[y_{i,t}^a=\beta_0^a+\beta_1^ax_{i,t'}^a+\epsilon_{i,t}^a\] avec:

• \(y_{i,t}\) le nombre d’entrées de la classe d’âge \(a\) à l’hôpital dans la région \(i\) sur la période \(t\), où \(t\) est une fenêtre de 7 jours.

• \(x_{i,t'}\) est le nombre de testés positifs de la classe d’âge \(a\) dans la région \(i\) sur la période \(t'\) où \(t'\) correspond à la fenêtre \(t\), décalé de 10 jours.

En d’autres termes, on fait ici un modèle de régression par classe d’âge, toute région confondue. Cela suppose que le lien entre les tests virologiques et le nombre d’hospitalisation est homogène dans une classe d’âge quelque soit les régions.

On merge avec le nombre de test positifs:

# débord on aggrège le nombre de testés positifs par région
test_by <- merge(test_by, dep_region, by = "dep")
test_reg <- aggregate(test_by[, c("tranche_9", "tranche_19", "tranche_29", "tranche_39", 
                                   "tranche_49", "tranche_59", "tranche_69", "tranche_79", 
                                   "tranche_89", "tranche_90", "tranche_0")], 
                      by = list(
  semaine = test_by$semaine,
  region = test_by$region), FUN = sum)
# ensuite, on fait le merge
my_basis_age_wide <- merge(my_basis_age_wide, test_reg, by = c("semaine", "region"))

Apprentissage:

On modélise sur les observations des semaines précédentes et on représente les résultats tranche d’âge par tranche d’âge

apprentissage_sample <- my_basis_age_wide[!(my_basis_age_wide$semaine %in% 
                                              c("semaine_t0-2", "semaine_t0-1", "semaine_t00")), ]
res_lm_9 <- lm(hosp_9 ~  tranche_9, data = apprentissage_sample)
res_lm_19 <- lm(hosp_19 ~  tranche_19, data = apprentissage_sample)
res_lm_29 <- lm(hosp_29 ~  tranche_29, data = apprentissage_sample)
res_lm_39 <- lm(hosp_39 ~  tranche_39, data = apprentissage_sample)
res_lm_49 <- lm(hosp_49 ~  tranche_49, data = apprentissage_sample)
res_lm_59 <- lm(hosp_59 ~  tranche_59, data = apprentissage_sample)
res_lm_69 <- lm(hosp_69 ~  tranche_69, data = apprentissage_sample)
res_lm_79 <- lm(hosp_79 ~  tranche_79, data = apprentissage_sample)
res_lm_89 <- lm(hosp_89 ~  tranche_89, data = apprentissage_sample)
res_lm_90 <- lm(hosp_90 ~  tranche_90, data = apprentissage_sample)

stargazer::stargazer(res_lm_9, res_lm_19, res_lm_29, res_lm_39, res_lm_49, res_lm_59,
                     res_lm_69, res_lm_79, res_lm_89, res_lm_90, type = "html")

	Dependent variable:
	hosp_9	hosp_19	hosp_29	hosp_39	hosp_49	hosp_59	hosp_69	hosp_79	hosp_89	hosp_90
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
tranche_9	0.015***
	(0.001)
tranche_19		0.004***
		(0.0002)
tranche_29			0.008***
			(0.0002)
tranche_39				0.014***
				(0.0003)
tranche_49					0.022***
					(0.0004)
tranche_59						0.047***
						(0.001)
tranche_69							0.105***
							(0.001)
tranche_79								0.221***
								(0.004)
tranche_89									0.342***
									(0.005)
tranche_90										0.284***
										(0.006)
Constant	0.658***	0.991***	2.820***	3.714***	4.442***	5.088***	9.041***	12.898***	16.005***	10.461***
	(0.238)	(0.202)	(0.384)	(0.482)	(0.603)	(1.079)	(1.529)	(2.494)	(2.932)	(1.790)
Observations	546	546	546	546	546	546	546	546	546	546
R2	0.410	0.523	0.754	0.830	0.874	0.895	0.907	0.868	0.879	0.825
Adjusted R2	0.409	0.522	0.753	0.830	0.874	0.895	0.907	0.868	0.879	0.825
Residual Std. Error (df = 544)	4.563	3.953	7.630	9.696	12.099	21.605	30.538	49.374	57.204	34.907
F Statistic (df = 1; 544)	378.536***	597.132***	1,664.881***	2,662.771***	3,785.032***	4,634.831***	5,287.015***	3,580.142***	3,949.153***	2,567.825***
Note:	p<0.1; p<0.05; p<0.01

Test:

On teste le modèle sur les données de la semaine actuelle. On revient sur les données départementales, on suppose donc que les modèles estimés pour chaque tranche d’âge sur les régions est valable aussi pour les départements.

test_sample <- my_basis[my_basis$semaine == "semaine_t00", ]
pred_9 <- predict(res_lm_9, newdata = test_sample)
pred_19 <- predict(res_lm_19, newdata = test_sample)
pred_29 <- predict(res_lm_29, newdata = test_sample)
pred_39 <- predict(res_lm_39, newdata = test_sample)
pred_49 <- predict(res_lm_49, newdata = test_sample)
pred_59 <- predict(res_lm_59, newdata = test_sample)
pred_69 <- predict(res_lm_69, newdata = test_sample)
pred_79 <- predict(res_lm_79, newdata = test_sample)
pred_89 <- predict(res_lm_89, newdata = test_sample)
pred_90 <- predict(res_lm_90, newdata = test_sample)

On a donc une prédiction par tranche d’âge et pour obtenir la prédiction finale, il faut donc faire la somme sur les différentes prédictions :

pred_2 <- pred_9 + pred_19 + pred_29 + pred_39 + pred_49 + pred_59 + pred_69 + 
  pred_79 + pred_89 + pred_90

plot(pred_2, my_basis[my_basis$semaine == "semaine_t00", "hosp"],
     xlab = "valeurs prédites", ylab = "valeurs observées")
abline(a = 0, b = 1)
text(pred_2, my_basis[my_basis$semaine == "semaine_t00", "hosp"], 
     my_basis[my_basis$semaine == "semaine_t00", "dep"], pos = 2)

L’écart quadratique moyen est égal ici à :

mean((pred_2 - my_basis[my_basis$semaine == "semaine_t00", "hosp"]) ^ 2, na.rm = T)

## [1] 4209.832

5.3 Modèle de série temporelle

On utilise la même stratégie que celle présentée pour prédire le nombre de cas positifs.

Etape d’apprentissage : on entraîne l’agorithme sur les données passées en enlevant la dernière semaine observée et on prédit sur cette semaine afin de calculer les écarts quadratiques avec les valeurs observées.

nom_dep <- my_basis[my_basis$semaine == "semaine_t00", "dep"]
pred_3a <- numeric(length(nom_dep))
pred_3b <- numeric(length(nom_dep))
pred_3c <- numeric(length(nom_dep))
for (k in 1:length(nom_dep)) {
  temp <- hospital[!(hospital$semaine %in% c("semaine_t0-2", "semaine_t0-1", "semaine_t00")) & 
                     hospital$dep == nom_dep[k], ]
  my_ts <- zoo(temp$incid_hosp, temp$jour)
  my_ts_diff <- diff(my_ts)
  # tseries::adf.test(my_ts) 
  # tseries::adf.test(my_ts_diff)
  if (nom_dep[k] %in% c("975", "977", "978")) {
    pred_3[k] <- NA
  } else {
    my_mod <- forecast::auto.arima(my_ts_diff)
    forecast_my_mod <- as.numeric(forecast(my_mod)$mean)
    pred_3a[k] <- sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:7])
    # modèles exponentiels
    # Méthode 2 : lissage exponentiel
    my_mod_exp <- ets(my_ts)
    forecast_my_mod_exp <- as.numeric(forecast(my_mod_exp)$mean)
    forecast_my_mod_exp <- ifelse(forecast_my_mod_exp > 0, forecast_my_mod_exp, 0)
    pred_3b[k] <- round(sum(forecast_my_mod_exp[1:7]), 0)
    # Méthode 3 : lissage exponentiel sur données hebdomadaires
    temp <- my_basis[my_basis$dep == nom_dep[k] & !(my_basis$semaine %in% 
                                          c("semaine_t0-2", "semaine_t0-1", "semaine_t00")), ]
    my_ts_exp <- zoo(temp$hosp, temp$jour)
    my_mod_exp_2 <- ets(my_ts_exp)
    forecast_my_mod_exp <- as.numeric(forecast(my_mod_exp_2)$mean)
    forecast_my_mod_exp <- ifelse(forecast_my_mod_exp > 0, forecast_my_mod_exp, 0)
    pred_3c[k] <- round(forecast_my_mod_exp[1], 0)
  }
}

On obtient le graphique suivant de valeurs prédites/valeurs observées :

op <- par(mfrow = c(1, 3), oma = c(0, 0, 0, 0))
plot(pred_3a, my_basis[my_basis$semaine == "semaine_t00", "hosp"],
     xlab = "valeurs prédites", ylab = "valeurs observées", main = "Box-Jenkins")
abline(a = 0, b = 1)
text(pred_3a, my_basis[my_basis$semaine == "semaine_t00", "hosp"], 
     my_basis[my_basis$semaine == "semaine_t00", "dep"], pos = 2)
plot(pred_3b, my_basis[my_basis$semaine == "semaine_t00", "hosp"],
     xlab = "valeurs prédites", ylab = "valeurs observées", main = "Lissage exponentiel journalier")
abline(a = 0, b = 1)
text(pred_3b, my_basis[my_basis$semaine == "semaine_t00", "hosp"], 
     my_basis[my_basis$semaine == "semaine_t00", "dep"], pos = 2)
plot(pred_3c, my_basis[my_basis$semaine == "semaine_t00", "hosp"],
     xlab = "valeurs prédites", ylab = "valeurs observées", main = "Lissage exponentiel hebdomadaire")
abline(a = 0, b = 1)
text(pred_3c, my_basis[my_basis$semaine == "semaine_t00", "hosp"], 
     my_basis[my_basis$semaine == "semaine_t00", "dep"], pos = 2)

par(op)

L’écart quadratique moyen est égal ici à :

c(mean((pred_3a - my_basis[my_basis$semaine == "semaine_t00", "hosp"]) ^ 2, na.rm = T),
  mean((pred_3b - my_basis[my_basis$semaine == "semaine_t00", "hosp"]) ^ 2, na.rm = T),
  mean((pred_3c - my_basis[my_basis$semaine == "semaine_t00", "hosp"]) ^ 2, na.rm = T)
)

## [1] 1298.9678 1203.5842  824.2376

Les 3 prédictions sont très proches et on va choisir un algorithme de type stepwise sur les prédictions pour choisir la meilleure combinaison des modèles de séries temporelles.

lm_3_ts <- step(lm(my_basis[my_basis$semaine == "semaine_t00", "hosp"] ~ pred_3a + pred_3b + pred_3c - 1))

## Start:  AIC=683.87
## my_basis[my_basis$semaine == "semaine_t00", "hosp"] ~ pred_3a + 
##     pred_3b + pred_3c - 1
## 
##           Df Sum of Sq   RSS    AIC
## - pred_3b  1      26.5 83034 681.90
## - pred_3a  1     232.4 83240 682.15
## <none>                 83007 683.87
## - pred_3c  1   11171.6 94179 694.62
## 
## Step:  AIC=681.9
## my_basis[my_basis$semaine == "semaine_t00", "hosp"] ~ pred_3a + 
##     pred_3c - 1
## 
##           Df Sum of Sq    RSS    AIC
## - pred_3a  1     210.4  83244 680.16
## <none>                  83034 681.90
## - pred_3c  1   22656.0 105690 704.27
## 
## Step:  AIC=680.16
## my_basis[my_basis$semaine == "semaine_t00", "hosp"] ~ pred_3c - 
##     1
## 
##           Df Sum of Sq     RSS     AIC
## <none>                   83244  680.16
## - pred_3c  1   2130151 2213395 1009.49

pred_3 <- predict(lm_3_ts)
mean((pred_3 - na.omit(my_basis[my_basis$semaine == "semaine_t00", "hosp"])) ^ 2)

## [1] 824.1998

On a donc 3 prédictions obtenues selon :

• modèle par région
• modèle par classe d’âge
• modèle de séries temporelles (lui-même combinaison de plusieurs méthodes)

5.4 Combinaison des prédictions

Combinaison des prédictions:

• pour prédire les nouvelles hospitalisations la semaine à venir, on va faire un panaché des trois prédictions en donnant plus de poids à la prédiction qui a le mieux marcher sur la semaine \(t_0\). Autrement dit, on fait un modèle linéaire (avec une procédure stepwise) du nombre d’hospitalisation en fonction des 3 méthodes de prédictions. On calcule l’écart quatratique moyen de la combinaison des prédictions.

lm_3 <- lm(my_basis[my_basis$semaine == "semaine_t00", "hosp"] ~ pred_1 + pred_2 + pred_3 - 1)
mean((predict(lm_3) - na.omit(my_basis[my_basis$semaine == "semaine_t00", "hosp"])) ^ 2)

## [1] 772.5462

• pour prédire les nouvelles hospitalisations la semaine d’après, on va utiliser une autre pondération en utilisant la même procédure que précédemment, mais dans une optique de prédire à deux semaines.

## Start:  AIC=1437.33
## y_true ~ pred_3a_s2 + pred_3b_s2 + pred_3c_s2 - 1
## 
##              Df Sum of Sq    RSS    AIC
## - pred_3b_s2  1       944 242304 1436.1
## - pred_3a_s2  1      1057 242417 1436.2
## <none>                    241361 1437.3
## - pred_3c_s2  1     37120 278480 1464.2
## 
## Step:  AIC=1436.12
## y_true ~ pred_3a_s2 + pred_3c_s2 - 1
## 
##              Df Sum of Sq    RSS    AIC
## - pred_3a_s2  1       502 242806 1434.5
## <none>                    242304 1436.1
## - pred_3c_s2  1     38733 281037 1464.1
## 
## Step:  AIC=1434.53
## y_true ~ pred_3c_s2 - 1
## 
##              Df Sum of Sq     RSS    AIC
## <none>                     242806 1434.5
## - pred_3c_s2  1   4183984 4426790 2019.0

5.5 Prédiction

On prédit le nombre d’hospitalisations :

• du [26 février 2021; 04 mars 2021] en utilisant les vrais valeurs du nombre de testé positifs la semaine du [16 février 2021; 22 février 2021].

• du [05 mars 2021; 11 mars 2021] en utilisant les valeurs prédites du nombre de testé positifs la semaine du [23 février 2021; 01 mars 2021].

Avant de faire cela, on actualise en incluant dans l’étape d’apprentissage les données de la dernière semaine observée:

# modèle 1
res_lm <- lm(hosp ~  tranche_0, data = my_basis[!(my_basis$semaine %in% "semaine_t0-1"), ])
# modèle 2
apprentissage_sample <- my_basis_age_wide[!(my_basis_age_wide$semaine %in% 
                                              c("semaine_t0-1")), ]
res_lm_9 <- lm(hosp_9 ~  tranche_9, data = apprentissage_sample)
res_lm_19 <- lm(hosp_19 ~  tranche_19, data = apprentissage_sample)
res_lm_29 <- lm(hosp_29 ~  tranche_29, data = apprentissage_sample)
res_lm_39 <- lm(hosp_39 ~  tranche_39, data = apprentissage_sample)
res_lm_49 <- lm(hosp_49 ~  tranche_49, data = apprentissage_sample)
res_lm_59 <- lm(hosp_59 ~  tranche_59, data = apprentissage_sample)
res_lm_69 <- lm(hosp_69 ~  tranche_69, data = apprentissage_sample)
res_lm_79 <- lm(hosp_79 ~  tranche_79, data = apprentissage_sample)
res_lm_89 <- lm(hosp_89 ~  tranche_89, data = apprentissage_sample)
res_lm_90 <- lm(hosp_90 ~  tranche_90, data = apprentissage_sample)

# On prédit avec la méthode 1 
new_data <- my_basis[my_basis$semaine %in% c("semaine_t0-1", "semaine_t0-2"), ]
pred_1 <- predict(res_lm, newdata = new_data)
# On prédit avec la méthode 2
test_sample <- my_basis[my_basis$semaine %in% c("semaine_t0-1", "semaine_t0-2"), ]
pred_9 <- predict(res_lm_9, newdata = test_sample)
pred_19 <- predict(res_lm_19, newdata = test_sample)
pred_29 <- predict(res_lm_29, newdata = test_sample)
pred_39 <- predict(res_lm_39, newdata = test_sample)
pred_49 <- predict(res_lm_49, newdata = test_sample)
pred_59 <- predict(res_lm_59, newdata = test_sample)
pred_69 <- predict(res_lm_69, newdata = test_sample)
pred_79 <- predict(res_lm_79, newdata = test_sample)
pred_89 <- predict(res_lm_89, newdata = test_sample)
pred_90 <- predict(res_lm_90, newdata = test_sample)
pred_2 <- pred_9 + pred_19 + pred_29 + pred_39 + pred_49 + pred_59 + pred_69 + 
  pred_79 + pred_89 + pred_90

# on prédit avec le modèle 3, mais on actualise les prédictions semaine par semaine
pred_3 <- matrix(0, length(nom_dep), 2)
for (k in 1:length(nom_dep)) {
 if (nom_dep[k] %in% c("975", "977", "978")) {
    pred_3[k, ] <- NA
  } else {
    temp <- hospital[!(hospital$semaine %in% c("semaine_t0-2", "semaine_t0-1")) & 
                     hospital$dep == nom_dep[k], ]
    my_ts <- zoo(temp$incid_hosp, temp$jour)
    my_ts_diff <- diff(my_ts)
    # tseries::adf.test(my_ts) 
    # tseries::adf.test(my_ts_diff)
    # predictions à 7 jours
    my_mod <- forecast::auto.arima(my_ts_diff)
    forecast_my_mod <- as.numeric(forecast(my_mod, h = 14)$mean)
    pred_3a_s1 <- sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:7])
    # prediction à 14 jours
    pred_3a_s2 <- sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:14]) - pred_3a_s1
    # Lissage exponentiel
    my_mod_exp <- ets(my_ts)
    forecast_my_mod_exp <- as.numeric(forecast(my_mod_exp, h = 14)$mean)
    forecast_my_mod_exp <- ifelse(forecast_my_mod_exp > 0, forecast_my_mod_exp, 0)
    pred_3b_s1 <- round(sum(forecast_my_mod_exp[1:7]), 0)
    pred_3b_s2 <- round(sum(forecast_my_mod_exp[1:14]), 0) - pred_3b_s1
    # Méthode 3 : lissage exponentiel sur données hebdomadaires
    temp <- my_basis[my_basis$dep == nom_dep[k] & !(my_basis$semaine %in% 
                                          c("semaine_t0-2", "semaine_t0-1")), ]
    my_ts_exp <- zoo(temp$hosp, temp$jour)
    my_mod_exp_2 <- ets(my_ts_exp)
    forecast_my_mod_exp <- as.numeric(forecast(my_mod_exp_2)$mean)
    forecast_my_mod_exp <- ifelse(forecast_my_mod_exp > 0, forecast_my_mod_exp, 0)
    pred_3c_s1 <- round(forecast_my_mod_exp[1], 0)
    pred_3c_s2 <- round(forecast_my_mod_exp[2], 0)
    
    # prédictions des time series
    pred_3[k, 1] <- predict(lm_3_ts, newdata = data.frame(pred_3a = pred_3a_s1,
                                                 pred_3b = pred_3b_s1,
                                                 pred_3c = pred_3c_s1))
    
    # prediction à 14 jours
    pred_3[k, 2] <- predict(lm_3b_ts, newdata = data.frame(pred_3a_s2 = pred_3a_s2,
                                                 pred_3b_s2 = pred_3b_s2,
                                                 pred_3c_s2 = pred_3c_s2))
  }
}
pred_3 <- as.vector(pred_3)
# On fait le mélande des deux prédictions
res_pred_a <- predict(lm_3, newdata = data.frame(pred_1 = pred_1[new_data$semaine == "semaine_t0-1"], 
                                               pred_2 = pred_2[test_sample$semaine == "semaine_t0-1"],
                                               pred_3 = pred_3[1:(length(pred_3) / 2)]))
res_pred_b <- predict(lm_3b, newdata = data.frame(
  pred_1_s2 = pred_1[new_data$semaine == "semaine_t0-2"],
  pred_2_s2 = pred_2[test_sample$semaine == "semaine_t0-2"],
  pred_3_s2 = pred_3[((length(pred_3) / 2) + 1):length(pred_3)]))
new_data <- my_basis[my_basis$semaine %in% "semaine_t0-1", ]
my_basis[my_basis$semaine %in% "semaine_t0-1", "hosp"] <- res_pred_a
my_basis[my_basis$semaine %in% "semaine_t0-2", "hosp"] <- res_pred_b
new_data$next_week <- res_pred_a
new_data$next_two_week <- res_pred_b

On va représenter l’évolution du nombre de nouveaux patients hospitalisés dans un intervalle de temps de 4 semaines :

• la semaine du [12 février 2021; 18 février 2021]
• les 7 derniers jours passés : [19 février 2021; 25 février 2021]
• la semaine à venir : [26 février 2021; 04 mars 2021]
• la semaine suivante à venir : [05 mars 2021; 11 mars 2021]

new_data[, "last_week"] <- my_basis[my_basis$semaine == "semaine_t01", "hosp"]
new_data[, "this_week"] <- my_basis[my_basis$semaine == "semaine_t00", "hosp"]
new_data_long <- tidyr::pivot_longer(data = select(new_data, dep, region, last_week, this_week, next_week, next_two_week),
                                   col = 3:6,
                                   names_to = "semaine",
                                   values_to = "hospitalisations")
new_data_long$semaine <- factor(new_data_long$semaine,
      levels = c("last_week", "this_week", "next_week", "next_two_week"),
      labels = c(paste0("[", format(to_day - 14, '%d %b'), "; ",  
                        format(to_day - 8, '%d %b'), "]"),
                 paste0("[", format(to_day - 7, '%d %b'), "; ",  
                        format(to_day - 1, '%d %b'), "]"),
                 paste0("[", format(to_day, '%d %b'), "; ",  
                        format(to_day + 6, '%d %b'), "]"),
                    paste0("[", format(to_day + 7, '%d %b'), "; ",  
                        format(to_day + 13, '%d %b'), "]"))
      )
# On ajoute aux données de la semaine dernière :
new_data_long$region <- factor(new_data_long$region, levels = hosp_region$region)
p <- ggplot(new_data_long, aes(x = semaine, y = hospitalisations, group = dep))+
    geom_line() +
  facet_wrap(~region)
plotly::ggplotly(p)

On aggrège les données à la France entière:

  my_basis_fr <- my_basis %>%
    group_by(semaine, jour) %>%
    summarise(hosp = sum(hosp),
              rea = sum(rea),
              dc = sum(dc))
  p <- ggplot(data = filter(my_basis_fr, semaine %in% c("semaine_t0-2", "semaine_t0-1", "semaine_t00")),
              aes(x = jour, y = hosp)) +
    geom_line(col = "red") +
    geom_line(data = filter(my_basis_fr, !(semaine %in% c("semaine_t0-2", "semaine_t0-1"))), 
              aes(x = jour, y = hosp)) +
  labs(title = "Prédiction des nouvelles hospitalisations dans les 14 jours",
       x = "semaine",
       y = "hospitalisations",
       fill = "Age") 
plotly::ggplotly(p)

6 Prédire le nombre de réanimations

L’idée est d’expliquer le nombre de nouvelles réanimations la semaine \(t\) par le nombre de nouvelles hospitalisations la semaine \(t-1\).

Ainsi on sera en mesure de prédire le nombre de nouvelles réanimations d’une part la semaine à venir, mais aussi la semaine d’après si on utilise les prédictions du nombre d’hospitalisation la semaine à venir.

On prépare les données et on représente le nombre de nouvelles réanimations par semaine et par département en fonction du nombre de nouvelles hospitalisations la semaine d’avant et on constate un lien très fort.

my_basis_temp <- my_basis %>% 
  filter(semaine == "semaine_t0-2")
my_basis_temp$hosp <- NA
my_basis_temp$semaine <- "semaine_t0-3"
my_basis_temp$jour <- my_basis_temp$jour + 7
my_basis_temp[, paste0("tranche_", c(9, 19, 29, 39, 49, 59, 69, 79, 89, 90, 0))] <- NA
my_basis <- rbind(my_basis_temp, my_basis)
my_basis_rea <- my_basis %>%
  select(dep, semaine, jour, region, rea)
temp_hosp <- my_basis %>%
  select(dep, jour, hosp) %>%
  mutate(jour = jour + 7)
my_basis_rea <- merge(my_basis_rea, temp_hosp, by = c("jour", "dep"), all.x = T)
my_basis_rea <- my_basis_rea %>%
  as.data.frame
my_basis_rea <- my_basis_rea[order(my_basis_rea$jour, decreasing = T), ]

p <- ggplot(my_basis_rea) +                
  aes(x = hosp, y = rea) +     
  geom_point() +                  
  geom_smooth(method = "loess") + 
  geom_smooth(method = "lm",     
              col = "red") +
  facet_wrap(~ region)
plotly::ggplotly(p)

On ne va faire que deux modèles :

• un modèle régional où on explique les nouvelles réanimations des départements au sein d’une même région.

• un modèle de série temporelles où on explique dans un département les réanimations à l’instant \(t\) par les valeurs du passé.

On n’utilise pas le modèle qui utilise les classes d’âges car c’est difficile d’avoir le nombre de nouvelles réanimations par jour/département par classe d’âge. Il se peut donc que les prédictions soient sous-estimées dans le cas où la distribution des patients hospitalisés agés évolue positivement au cours du temps.

6.1 Modèle 1 : modèle linéaire

Apprentissage:

On modélise sur les observations des semaines précédentes:

res_lm_rea_1 <- lm(rea ~  region + hosp:region - 1, 
             data = my_basis_rea[!(my_basis_rea$semaine %in% c("semaine_t0-2", "semaine_t0-1", "semaine_t00")), ])

stargazer::stargazer(res_lm_rea_1, type = "html")

	Dependent variable:
	rea
regionAuvergne-Rhône-Alpes	-0.557
	(0.387)
regionBourgogne-Franche-Comté	0.885*
	(0.508)
regionBretagne	0.798
	(0.725)
regionCentre-Val de Loire	0.066
	(0.624)
regionCorse	0.453
	(1.040)
regionDOM-TOM	1.593**
	(0.627)
regionGrand Est	-0.149
	(0.463)
regionHauts-de-France	-0.342
	(0.619)
regionIle-de-France	-0.262
	(0.608)
regionNormandie	0.551
	(0.631)
regionNouvelle-Aquitaine	-0.008
	(0.396)
regionOccitanie	-0.147
	(0.371)
regionPays de la Loire	0.614
	(0.704)
regionProvence-Alpes-Côte d’Azur	-1.086*
	(0.557)
regionAuvergne-Rhône-Alpes:hosp	0.156***
	(0.002)
regionBourgogne-Franche-Comté:hosp	0.116***
	(0.007)
regionBretagne:hosp	0.109***
	(0.015)
regionCentre-Val de Loire:hosp	0.160***
	(0.013)
regionCorse:hosp	0.196*
	(0.104)
regionDOM-TOM:hosp	0.115***
	(0.013)
regionGrand Est:hosp	0.145***
	(0.005)
regionHauts-de-France:hosp	0.176***
	(0.003)
regionIle-de-France:hosp	0.190***
	(0.003)
regionNormandie:hosp	0.123***
	(0.008)
regionNouvelle-Aquitaine:hosp	0.150***
	(0.008)
regionOccitanie:hosp	0.206***
	(0.006)
regionPays de la Loire:hosp	0.124***
	(0.011)
regionProvence-Alpes-Côte d’Azur:hosp	0.162***
	(0.003)
Observations	3,838
R2	0.890
Adjusted R2	0.889
Residual Std. Error	7.024 (df = 3810)
F Statistic	1,102.491*** (df = 28; 3810)
Note:	p<0.1; p<0.05; p<0.01

Test:

On teste le modèle sur les données de la semaine actuelle:

pred_rea_1 <- predict(res_lm_rea_1, newdata = my_basis_rea[my_basis_rea$semaine == "semaine_t00", ])

plot(pred_rea_1, my_basis_rea[my_basis_rea$semaine == "semaine_t00", "rea"],
     xlab = "valeurs prédites", ylab = "valeurs observées")
abline(a = 0, b = 1)
text(pred_rea_1, my_basis_rea[my_basis_rea$semaine == "semaine_t00", "rea"], 
     my_basis_rea[my_basis_rea$semaine == "semaine_t00", "dep"], pos = 2)

L’écart quadratique moyen est égal ici à :

mean((pred_rea_1 - my_basis_rea[my_basis_rea$semaine == "semaine_t00", "rea"]) ^ 2, na.rm = T)

## [1] 135.1014

6.2 Modèle 2 : série temporelle

On utilise la même stratégie que celle présentée pour prédire le nombre de nouveaux cas positifs et de nouvelles réanimations.

Etape d’apprentissage : on entraîne l’agorithme sur les données passées en enlevant la dernière semaine observée et on prédit sur cette semaine afin de calculer les écarts quadratiques avec les valeurs observées.

nom_dep <- my_basis_rea[my_basis_rea$semaine == "semaine_t00", "dep"]
pred_rea_2a <- numeric(length(nom_dep))
pred_rea_2b <- numeric(length(nom_dep))
pred_rea_2c <- numeric(length(nom_dep))
for (k in 1:length(nom_dep)) {
  temp <- hospital[!(hospital$semaine %in% c("semaine_t0-2", "semaine_t0-1", "semaine_t00")) & 
                     hospital$dep == nom_dep[k], ]
  my_ts <- zoo(temp$incid_rea, temp$jour)
  my_ts_diff <- diff(my_ts)
  # tseries::adf.test(my_ts) 
  # tseries::adf.test(my_ts_diff)
  if (nom_dep[k] %in% c("975", "977", "978")) {
    pred_rea_2[k] <- NA
  } else {
    # box jenkins
    my_mod <- forecast::auto.arima(my_ts_diff)
    forecast_my_mod <- as.numeric(forecast(my_mod)$mean)
    pred_rea_2a[k] <- sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:7])
    # modèles exponentiels
    # Méthode 2 : lissage exponentiel
    my_mod_exp <- ets(my_ts)
    forecast_my_mod_exp <- as.numeric(forecast(my_mod_exp)$mean)
    forecast_my_mod_exp <- ifelse(forecast_my_mod_exp > 0, forecast_my_mod_exp, 0)
    pred_rea_2b[k] <- round(sum(forecast_my_mod_exp[1:7]), 0)
    # Méthode 3 : lissage exponentiel sur données hebdomadaires
    temp <- my_basis[my_basis$dep == nom_dep[k] & !(my_basis$semaine %in% 
                                          c("semaine_t0-3", "semaine_t0-2", "semaine_t0-1", "semaine_t00")), ]
    my_ts_exp <- zoo(temp$rea, temp$jour)
    my_mod_exp_2 <- ets(my_ts_exp)
    forecast_my_mod_exp <- as.numeric(forecast(my_mod_exp_2)$mean)
    forecast_my_mod_exp <- ifelse(forecast_my_mod_exp > 0, forecast_my_mod_exp, 0)
    pred_rea_2c[k] <- round(forecast_my_mod_exp[1], 0)
  }
}

On observe le graphique des valeurs prédites/valeurs observées :

op <- par(mfrow = c(1, 3), oma = c(0, 0, 0, 0))
plot(pred_rea_2a, my_basis_rea[my_basis_rea$semaine == "semaine_t00", "rea"],
     xlab = "valeurs prédites", ylab = "valeurs observées", main = "Box-Jenkins")
abline(a = 0, b = 1)
text(pred_rea_2a, my_basis_rea[my_basis_rea$semaine == "semaine_t00", "rea"], 
     my_basis_rea[my_basis_rea$semaine == "semaine_t00", "dep"], pos = 2)
plot(pred_rea_2b, my_basis_rea[my_basis_rea$semaine == "semaine_t00", "rea"],
     xlab = "valeurs prédites", ylab = "valeurs observées", main = "Lissage exponentiel journalier")
abline(a = 0, b = 1)
text(pred_rea_2b, my_basis_rea[my_basis_rea$semaine == "semaine_t00", "rea"], 
     my_basis_rea[my_basis_rea$semaine == "semaine_t00", "dep"], pos = 2)
plot(pred_rea_2c, my_basis_rea[my_basis_rea$semaine == "semaine_t00", "rea"],
     xlab = "valeurs prédites", ylab = "valeurs observées", main = "Lissage exponentiel hebdomadaire")
abline(a = 0, b = 1)
text(pred_rea_2c, my_basis_rea[my_basis_rea$semaine == "semaine_t00", "rea"], 
     my_basis_rea[my_basis_rea$semaine == "semaine_t00", "dep"], pos = 2)

L’écart quadratique moyen est égal ici à :

c(mean((pred_rea_2a - my_basis_rea[my_basis_rea$semaine == "semaine_t00", "rea"]) ^ 2, na.rm = T), 
  mean((pred_rea_2b - my_basis_rea[my_basis_rea$semaine == "semaine_t00", "rea"]) ^ 2, na.rm = T),
  mean((pred_rea_2c - my_basis_rea[my_basis_rea$semaine == "semaine_t00", "rea"]) ^ 2, na.rm = T)
)

## [1] 71.61796 73.03960 49.22772

Les 3 prédictions sont très proches et on va choisir un algorithme de type stepwise sur les prédictions pour choisir la meilleure combinaison et ne conserver qu’une seule prédiction basée sur les séries temporelles:

lm_2_rea_ts <- step(lm(my_basis[my_basis$semaine == "semaine_t00", "rea"] ~ 
                         pred_rea_2a + pred_rea_2b + pred_rea_2c - 1))

## Start:  AIC=376.92
## my_basis[my_basis$semaine == "semaine_t00", "rea"] ~ pred_rea_2a + 
##     pred_rea_2b + pred_rea_2c - 1
## 
##               Df Sum of Sq    RSS    AIC
## <none>                     3974.3 376.92
## - pred_rea_2a  1     95.15 4069.4 377.31
## - pred_rea_2b  1    153.57 4127.9 378.75
## - pred_rea_2c  1   3094.69 7069.0 433.08

pred_rea_2 <- predict(lm_2_rea_ts)
mean((pred_rea_2 - na.omit(my_basis[my_basis$semaine == "semaine_t00", "rea"])) ^ 2)

## [1] 39.3493

6.3 Combinaison des prédictions

Combinaison des prédictions: on peut envisager de faire un panaché des deux prédictions. Autrement dit, on fait un modèle linéaire (avec une procédure stepwise) du nombre de réanimations observée la semaine t0 en fonction des 2 méthodes de prédictions. On obtient l’écart-quadratique moyen suivant:

lm_rea_3 <- lm(my_basis_rea[my_basis_rea$semaine == "semaine_t00", "rea"] ~ 
                 pred_rea_1 + pred_rea_2 - 1)
mean((predict(lm_rea_3) - na.omit(my_basis_rea[my_basis_rea$semaine == "semaine_t00", "rea"])) ^ 2)

## [1] 39.30859

On adapte le poids des prédictions en fonction de la semaine à prédire

semaine_to_drop <- c("semaine_t0-3", "semaine_t0-2", "semaine_t0-1", "semaine_t00")
pred_rea_1_s2 <- pred_rea_1
pred_rea_2a_s2 <- pred_rea_2a
pred_rea_2b_s2 <- pred_rea_2b
pred_rea_2c_s2 <- pred_rea_2c

y_true <- my_basis_rea[my_basis_rea$semaine == "semaine_t00", "rea"]

for (j in 0:0) {
  
  semaine_to_estim <-  paste0("semaine_t0", j)
  y_true <- c(y_true, my_basis[my_basis$semaine == semaine_to_estim, "rea"])
  semaine_to_drop <- c(semaine_to_drop, paste0("semaine_t0", j + 1))
  res_lm_rea_1 <- lm(rea ~  region + hosp:region - 1, 
             data = my_basis_rea[!(my_basis_rea$semaine %in% semaine_to_drop), ])
  pred_rea_1_s2 <- c(pred_rea_1_s2, 
     round(predict(res_lm_rea_1, newdata = my_basis_rea[my_basis_rea$semaine == semaine_to_estim, ])))
  pred_rea_2a_temp <- numeric(length(nom_dep))
  pred_rea_2b_temp <- numeric(length(nom_dep))
  pred_rea_2c_temp <- numeric(length(nom_dep))

  for (k in 1:length(nom_dep)) {
    temp <- hospital[!(hospital$semaine %in% semaine_to_drop) & 
                     hospital$dep == nom_dep[k], ]
    my_ts <- zoo(temp$incid_rea, temp$jour)
    my_ts_diff <- diff(my_ts)
    # tseries::adf.test(my_ts) 
    # tseries::adf.test(my_ts_diff)
    if (nom_dep[k] %in% c("975", "977", "978")) {
      pred_rea_2[k] <- NA
    } else {
      my_mod <- forecast::auto.arima(my_ts_diff)
      forecast_my_mod <- as.numeric(forecast(my_mod, h = 14)$mean)
      temp <- sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:7])
      pred_rea_2a_temp[k] <- sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:14]) - temp
      # modèles exponentiels
      # Méthode 2 : lissage exponentiel
      my_mod_exp <- ets(my_ts)
      forecast_my_mod_exp <- as.numeric(forecast(my_mod_exp, h = 14)$mean)
      forecast_my_mod_exp <- ifelse(forecast_my_mod_exp > 0, forecast_my_mod_exp, 0)
      temp <- round(sum(forecast_my_mod_exp[1:7]), 0)
      pred_rea_2b_temp[k] <- round(sum(forecast_my_mod_exp[1:14]), 0) - temp
      # Méthode 3 : lissage exponentiel sur données hebdomadaires
      temp <- my_basis[my_basis$dep == nom_dep[k] & !(my_basis$semaine %in% semaine_to_drop), ]
      my_ts_exp <- zoo(temp$rea, temp$jour)
      if (all(my_ts_exp == 0)) {
        pred_rea_2c_temp[k] <- 0
      } else {
        my_mod_exp_2 <- ets(my_ts_exp)
        forecast_my_mod_exp <- as.numeric(forecast(my_mod_exp_2)$mean)
        forecast_my_mod_exp <- ifelse(forecast_my_mod_exp > 0, forecast_my_mod_exp, 0)
        pred_rea_2c_temp[k] <- round(forecast_my_mod_exp[2], 0)
      }
    }
    
  }
   pred_rea_2a_s2 <- c(pred_rea_2a_s2, pred_rea_2a_temp)
   pred_rea_2b_s2 <- c(pred_rea_2b_s2, pred_rea_2b_temp)
   pred_rea_2c_s2 <- c(pred_rea_2c_s2, pred_rea_2c_temp)
}


lm_2_rea_ts_s1 <- step(lm(y_true ~ pred_rea_2a_s2 + pred_rea_2b_s2 + pred_rea_2c_s2 - 1))

## Start:  AIC=834.73
## y_true ~ pred_rea_2a_s2 + pred_rea_2b_s2 + pred_rea_2c_s2 - 1
## 
##                  Df Sum of Sq   RSS    AIC
## <none>                        12221 834.73
## - pred_rea_2a_s2  1    687.18 12908 843.78
## - pred_rea_2b_s2  1   1096.31 13317 850.09
## - pred_rea_2c_s2  1   2128.89 14350 865.17

pred_rea_2_s2 <- predict(lm_2_rea_ts_s1)

lm_rea_3b <- lm(y_true ~ pred_rea_1_s2 + pred_rea_2_s2 - 1)



#######

semaine_to_drop <- c("semaine_t0-3", "semaine_t0-2", "semaine_t0-1", "semaine_t00", "semaine_t01")
pred_rea_1_s3 <- pred_rea_1
pred_rea_2a_s3 <- pred_rea_2a
pred_rea_2b_s3 <- pred_rea_2b
pred_rea_2c_s3 <- pred_rea_2c

y_true <- my_basis_rea[my_basis_rea$semaine == "semaine_t00", "rea"]

for (j in 0:0) {
  
  semaine_to_estim <-  paste0("semaine_t0", j)
  y_true <- c(y_true, my_basis[my_basis$semaine == semaine_to_estim, "rea"])
  semaine_to_drop <- c(semaine_to_drop, paste0("semaine_t0", j + 2))
  
  res_lm_rea_1 <- lm(rea ~  region + hosp:region - 1, 
             data = my_basis_rea[!(my_basis_rea$semaine %in% semaine_to_drop), ])
  pred_rea_1_s3 <- c(pred_rea_1_s3, round(predict(res_lm_rea_1, newdata = my_basis_rea[my_basis_rea$semaine == semaine_to_estim, ])))
  
  pred_rea_2a_temp <- numeric(length(nom_dep))
  pred_rea_2b_temp <- numeric(length(nom_dep))
  pred_rea_2c_temp <- numeric(length(nom_dep))

  for (k in 1:length(nom_dep)) {
     temp <- hospital[!(hospital$semaine %in% semaine_to_drop) & hospital$dep == nom_dep[k], ]
     my_ts <- zoo(temp$incid_rea, temp$jour)
     my_ts_diff <- diff(my_ts)
     # tseries::adf.test(my_ts) 
     # tseries::adf.test(my_ts_diff)
     if (nom_dep[k] %in% c("975", "977", "978")) {
       pred_rea_2[k] <- NA
     } else {
       my_mod <- forecast::auto.arima(my_ts_diff)
       forecast_my_mod <- as.numeric(forecast(my_mod, h = 21)$mean)
       temp1 <- sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:7])
       temp2 <- sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:14]) - temp1
       pred_rea_2a_temp[k] <- sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:21]) - temp1 - temp2
       # modèles exponentiels
       # Méthode 2 : lissage exponentiel
       my_mod_exp <- ets(my_ts)
       forecast_my_mod_exp <- as.numeric(forecast(my_mod_exp, h = 21)$mean)
       forecast_my_mod_exp <- ifelse(forecast_my_mod_exp > 0, forecast_my_mod_exp, 0)
       temp1 <- round(sum(forecast_my_mod_exp[1:7]), 0)
       temp2 <- round(sum(forecast_my_mod_exp[1:14]), 0) - temp1
       pred_rea_2b_temp[k] <- round(sum(forecast_my_mod_exp[1:21]), 0) - temp2 - temp1
       # Méthode 3 : lissage exponentiel sur données hebdomadaires
       temp <- my_basis[my_basis$dep == nom_dep[k] & !(my_basis$semaine %in% semaine_to_drop), ]
       my_ts_exp <- zoo(temp$rea, temp$jour)
       if (all(my_ts_exp == 0)) {
         pred_rea_2c_temp[k] <- 0
       } else {
         my_mod_exp_2 <- ets(my_ts_exp)
         forecast_my_mod_exp <- as.numeric(forecast(my_mod_exp_2)$mean)
         forecast_my_mod_exp <- ifelse(forecast_my_mod_exp > 0, forecast_my_mod_exp, 0)
         pred_rea_2c_temp[k] <- round(forecast_my_mod_exp[3], 0)
       }
    }
}

  pred_rea_2a_s3 <- c(pred_rea_2a_s3, pred_rea_2a_temp)
  pred_rea_2b_s3 <- c(pred_rea_2b_s3, pred_rea_2b_temp)
  pred_rea_2c_s3 <- c(pred_rea_2c_s3, pred_rea_2c_temp)
}

lm_2_rea_ts_s2 <- step(lm(y_true ~ pred_rea_2a_s3 + pred_rea_2b_s3 + pred_rea_2c_s3 - 1))

## Start:  AIC=869.47
## y_true ~ pred_rea_2a_s3 + pred_rea_2b_s3 + pred_rea_2c_s3 - 1
## 
##                  Df Sum of Sq   RSS    AIC
## <none>                        14514 869.47
## - pred_rea_2b_s3  1    221.20 14736 870.53
## - pred_rea_2a_s3  1    875.54 15390 879.31
## - pred_rea_2c_s3  1   2264.15 16778 896.76

pred_rea_2_s3 <- predict(lm_2_rea_ts_s2)

lm_rea_3c <- lm(y_true ~ pred_rea_1_s3 + pred_rea_2_s3 - 1)

6.4 Prédiction

On prédit:

• le nombre de réanimations à venir du [26 février 2021; 04 mars 2021] en utilisant les nouvelles hospitalisations du [19 février 2021; 25 février 2021]

• le nombre de réanimations à venir du [05 mars 2021; 11 mars 2021] en utilisant la prédiction des hospitalisations à venir du [26 février 2021; 04 mars 2021]

• le nombre de réanimations à venir du [12 mars 2021; 18 mars 2021] en utilisant la prédiction des hospitalisations à venir du [05 mars 2021; 11 mars 2021]

Pour cela, on actualise le modèle, c’est-à-dire qu’on inclut la dernière semaine observée:

res_lm <- lm(rea ~  region + hosp:region - 1, 
             data = my_basis_rea[!(my_basis_rea$semaine %in% c("semaine_t0-2", "semaine_t0-1")), ])

# semaine t+1
new_data_rea_1 <- my_basis_rea[my_basis_rea$semaine %in% c("semaine_t0-1", "semaine_t0-2", "semaine_t0-3"),  ]
pred_rea_1 <- predict(res_lm, newdata = new_data_rea_1)

pred_rea_2 <- matrix(0, length(nom_dep), 3)
pred_rea_2a <- matrix(0, length(nom_dep), 3)
pred_rea_2b <- matrix(0, length(nom_dep), 3)
pred_rea_2c <- matrix(0, length(nom_dep), 3)
for (k in 1:length(nom_dep)) {
  temp <- hospital[!(hospital$semaine %in% c("semaine_t0-3", "semaine_t0-2", "semaine_t0-1")) & 
                     hospital$dep == nom_dep[k], ]
  my_ts <- zoo(temp$incid_rea, temp$jour)
  my_ts_diff <- diff(my_ts)
  # tseries::adf.test(my_ts) 
  # tseries::adf.test(my_ts_diff)
  if (nom_dep[k] %in% c("975", "977", "978")) {
    pred_rea_2[k] <- NA
  } else {
    my_mod <- forecast::auto.arima(my_ts_diff)
    forecast_my_mod <- as.numeric(forecast(my_mod, h = 21)$mean)
    pred_3a_s1 <- sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:7])
    pred_3a_s2 <- sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:14]) - pred_3a_s1
    pred_3a_s3 <- sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:21]) - 
      pred_3a_s1 - pred_3a_s2
    # Lissage exponentiel
    my_mod_exp <- ets(my_ts)
    forecast_my_mod_exp <- as.numeric(forecast(my_mod_exp, h = 21)$mean)
    forecast_my_mod_exp <- ifelse(forecast_my_mod_exp > 0, forecast_my_mod_exp, 0)
    pred_3b_s1 <- round(sum(forecast_my_mod_exp[1:7]), 0)
    pred_3b_s2 <- round(sum(forecast_my_mod_exp[1:14]), 0) - pred_3b_s1
    pred_3b_s3 <- round(sum(forecast_my_mod_exp[1:21]), 0) - pred_3b_s2 - pred_3b_s1
    # Méthode 3 : lissage exponentiel sur données hebdomadaires
    temp <- my_basis[my_basis$dep == nom_dep[k] & !(my_basis$semaine %in% 
                                          c("semaine_t0-3", "semaine_t0-2", "semaine_t0-1")), ]
    my_ts_exp <- zoo(temp$rea, temp$jour)
    my_mod_exp_2 <- ets(my_ts_exp)
    forecast_my_mod_exp <- as.numeric(forecast(my_mod_exp_2)$mean)
    forecast_my_mod_exp <- ifelse(forecast_my_mod_exp > 0, forecast_my_mod_exp, 0)
    pred_3c_s1 <- round(forecast_my_mod_exp[1], 0)
    pred_3c_s2 <- round(forecast_my_mod_exp[2], 0)
    pred_3c_s3 <- round(forecast_my_mod_exp[3], 0)    
    
    pred_rea_2[k, 1] <- predict(lm_2_rea_ts, newdata = data.frame(pred_rea_2a = pred_3a_s1,
                                                 pred_rea_2b = pred_3b_s1,
                                                 pred_rea_2c = pred_3c_s1))
    pred_rea_2[k, 2] <- predict(lm_2_rea_ts_s1, newdata = data.frame(pred_rea_2a_s2 = pred_3a_s2,
                                                 pred_rea_2b_s2 = pred_3b_s2,
                                                 pred_rea_2c_s2 = pred_3c_s2))
    pred_rea_2[k, 3] <- predict(lm_2_rea_ts_s2, newdata = data.frame(pred_rea_2a_s3 = pred_3a_s3,
                                                 pred_rea_2b_s3 = pred_3b_s3,
                                                 pred_rea_2c_s3 = pred_3c_s3))
  }
}

pred_rea_a <- predict(lm_rea_3, newdata = data.frame(pred_rea_1 = 
                        pred_rea_1[new_data_rea_1$semaine == "semaine_t0-1"],
                        pred_rea_2 = as.vector(pred_rea_2)[1:(length(pred_rea_1) / 3)]))

pred_rea_b <- predict(lm_rea_3b, newdata = data.frame(
  pred_rea_1_s2 = pred_rea_1[new_data_rea_1$semaine == "semaine_t0-2"],
  pred_rea_2_s2 = as.vector(pred_rea_2)[((length(pred_rea_1) / 3) + 1):(2 * length(pred_rea_1) / 3)]))

pred_rea_c <- predict(lm_rea_3c, newdata = data.frame(
  pred_rea_1_s3 = pred_rea_1[new_data_rea_1$semaine == "semaine_t0-3"],
  pred_rea_2_s3 = as.vector(pred_rea_2)[(2 * length(pred_rea_1) / 3 + 1):length(pred_rea_1)]))

# on synthétise les résultats
new_data <- my_basis[my_basis$semaine %in% "semaine_t0-1", ]
new_data$this_week <- my_basis_rea[my_basis_rea$semaine == "semaine_t00", "rea"]
new_data$next_week <- pred_rea_a
new_data$next_two_week <- pred_rea_b
new_data$next_three_week <- pred_rea_c
my_basis[my_basis$semaine %in% "semaine_t0-1", "rea"] <- pred_rea_a
my_basis[my_basis$semaine %in% "semaine_t0-2", "rea"] <- pred_rea_b
my_basis[my_basis$semaine %in% "semaine_t0-3", "rea"] <- pred_rea_c

On va représenter l’évolution du nombre de patients en réanimations dans un intervalle de temps de 4 semaines :

• les 7 derniers jours passés : [19 février 2021; 25 février 2021]
• la semaine à venir : [26 février 2021; 04 mars 2021]
• la 2ème semaine à venir : [05 mars 2021; 11 mars 2021]
• la 3ème semaine à venir : [12 mars 2021; 18 mars 2021]

new_data_long <- tidyr::pivot_longer(data = select(new_data, dep, region, 
                                   this_week, next_week,  next_two_week, next_three_week),
                                   col = 3:6,
                                   names_to = "semaine",
                                   values_to = "rea")
new_data_long$semaine <- factor(new_data_long$semaine,
      levels = c("this_week", "next_week", "next_two_week", "next_three_week"),
      labels = c(paste0("[", format(to_day - 7, '%d %b'), "; ",  
                        format(to_day - 1, '%d %b'), "]"),
                 paste0("[", format(to_day, '%d %b'), "; ",  
                        format(to_day + 6, '%d %b'), "]"),
                 paste0("[", format(to_day+7, '%d %b'), "; ",  
                        format(to_day + 13, '%d %b'), "]"), 
                 paste0("[", format(to_day + 14, '%d %b'), "; ",  
                        format(to_day + 20, '%d %b'), "]")
                 )
      )

new_data_long$region <- factor(new_data_long$region, levels = hosp_region$region)
p <- ggplot(new_data_long, aes(x = semaine, y = rea,  group = dep))+
    geom_line() +
  facet_wrap(~region)
plotly::ggplotly(p)

On aggrège les données à la France entière:

my_basis_fr <- my_basis %>%
  group_by(semaine, jour) %>%
  summarise(rea = sum(rea))
p <- ggplot(data = filter(my_basis_fr, semaine %in% 
                      c("semaine_t0-3", "semaine_t0-2", "semaine_t0-1", "semaine_t00")),
            aes(x = jour, y = rea)) +
  geom_line(col = "red") +
  geom_line(data = filter(my_basis_fr, !(semaine %in% 
                        c("semaine_t0-3", "semaine_t0-2", "semaine_t0-1"))), 
            aes(x = jour, y = rea)) +
  labs(title = "Prédiction des nouvelles réanimations dans les 21 jours",
       x = "semaine",
       y = "réanimations",
       fill = "Age") 
plotly::ggplotly(p)

7 Prédire le nombre de décès

L’idée est d’expliquer le nombre de nouveaux décès la semaine \(t\) par les nouvelles réanimations la semaine \(t-1\).

Ainsi on sera en mesure de prédire le nombre de nouveaux décès la semaine à venir, mais aussi les trois semaines suivantes en utilisant les prédictions des hospitalisations, des réanimations et cas positifs.

On prépare les données et on représente le nombre de nouveaux décès par semaine et par département en fonction du nombre de nouvelles réanimations la semaine d’avant et on constate un lien très fort.

my_basis_temp <- my_basis %>% 
  filter(semaine == "semaine_t0-3")
my_basis_temp$rea <- NA
my_basis_temp$semaine <- "semaine_t0-4"
my_basis_temp$jour <- my_basis_temp$jour + 7
my_basis <- rbind(my_basis_temp, my_basis)
my_basis_dc <- my_basis %>%
  select(dep, semaine, jour, region, dc)
temp_rea <- my_basis %>%
  select(dep, jour, rea) %>%
  mutate(jour = jour + 7)
my_basis_dc <- merge(my_basis_dc, temp_rea, by = c("jour", "dep"), all.x = T)
my_basis_dc <- my_basis_dc %>%
  as.data.frame
my_basis_dc <- my_basis_dc[order(my_basis_dc$jour, decreasing = T), ]

p <- ggplot(my_basis_dc) +                
  aes(x = rea, y = dc) +     
  geom_point() +                  
  geom_smooth(method = "loess") + 
  geom_smooth(method = "lm",     
              col = "red") +
  facet_wrap(~ region)
plotly::ggplotly(p)

On va faire deux modèles : un modèle régional où on explique les nouvelles réanimations des départements au sein d’une même région ainsi qu’un modèle de série temporelle département par département.

7.1 Modèle 1 : modèle linéaire

Apprentissage:

On modélise sur les observations des semaines précédentes:

res_lm_dc_1 <- lm(dc ~  region + rea:region - 1, 
             data = my_basis_dc[!(my_basis_dc$semaine %in% 
                c("semaine_t0-3", "semaine_t0-2", "semaine_t0-1", "semaine_t00")), ])

stargazer::stargazer(res_lm_dc_1, type = "html")

	Dependent variable:
	dc
regionAuvergne-Rhône-Alpes	3.766***
	(0.420)
regionBourgogne-Franche-Comté	2.878***
	(0.543)
regionBretagne	1.460*
	(0.796)
regionCentre-Val de Loire	3.374***
	(0.627)
regionCorse	0.264
	(1.080)
regionDOM-TOM	-0.377
	(0.736)
regionGrand Est	2.245***
	(0.495)
regionHauts-de-France	5.542***
	(0.670)
regionIle-de-France	7.871***
	(0.624)
regionNormandie	1.062
	(0.693)
regionNouvelle-Aquitaine	1.926***
	(0.418)
regionOccitanie	1.612***
	(0.400)
regionPays de la Loire	1.972***
	(0.734)
regionProvence-Alpes-Côte d’Azur	3.973***
	(0.602)
regionAuvergne-Rhône-Alpes:rea	0.972***
	(0.016)
regionBourgogne-Franche-Comté:rea	0.991***
	(0.050)
regionBretagne:rea	0.997***
	(0.118)
regionCentre-Val de Loire:rea	0.548***
	(0.069)
regionCorse:rea	0.544
	(0.367)
regionDOM-TOM:rea	0.532***
	(0.103)
regionGrand Est:rea	1.226***
	(0.037)
regionHauts-de-France:rea	0.871***
	(0.018)
regionIle-de-France:rea	0.600***
	(0.016)
regionNormandie:rea	1.301***
	(0.063)
regionNouvelle-Aquitaine:rea	0.802***
	(0.050)
regionOccitanie:rea	0.631***
	(0.032)
regionPays de la Loire:rea	1.006***
	(0.077)
regionProvence-Alpes-Côte d’Azur:rea	0.904***
	(0.017)
Observations	3,838
R2	0.859
Adjusted R2	0.858
Residual Std. Error	7.868 (df = 3810)
F Statistic	829.742*** (df = 28; 3810)
Note:	p<0.1; p<0.05; p<0.01

Test:

On teste le modèle sur les données de la semaine actuelle:

pred_dc_1 <- predict(res_lm_dc_1, newdata = my_basis_dc[my_basis_dc$semaine == "semaine_t00", ])

plot(pred_dc_1, my_basis_dc[my_basis_dc$semaine == "semaine_t00", "dc"],
     xlab = "valeurs prédites", ylab = "valeurs observées")
abline(a = 0, b = 1)
text(pred_dc_1, my_basis_dc[my_basis_dc$semaine == "semaine_t00", "dc"], 
     my_basis_dc[my_basis_dc$semaine == "semaine_t00", "dep"], pos = 2)

L’écart quadratique moyen est égal ici à :

mean((pred_dc_1 - my_basis_dc[my_basis_dc$semaine == "semaine_t00", "dc"]) ^ 2, na.rm = T)

## [1] 62.58937

7.2 Modèle 2 : série temporelle

On utilise la même stratégie que celle présentée pour prédire le nombre de nouveaux cas, de nouvelles hospitalisations et de nouvelles réanimations.

Etape d’apprentissage : on entraîne l’agorithme sur les données passées en enlevant la dernière semaine observée et on prédit sur cette semaine afin de calculer les écarts quadratiques avec les valeurs observées.

pred_dc_2a <- numeric(length(nom_dep))
pred_dc_2b <- numeric(length(nom_dep))
pred_dc_2c <- numeric(length(nom_dep))
for (k in 1:length(nom_dep)) {
  temp <- hospital[!(hospital$semaine %in% c("semaine_t0-1", "semaine_t00")) & 
                     hospital$dep == nom_dep[k], ]
  my_ts <- zoo(temp$incid_dc, temp$jour)
  my_ts_diff <- diff(my_ts)
  # tseries::adf.test(my_ts) 
  # tseries::adf.test(my_ts_diff)
  if (nom_dep[k] %in% c("975", "977", "978")) {
    pred_dc_2[k] <- NA
  } else {
    my_mod <- forecast::auto.arima(my_ts_diff)
    forecast_my_mod <- as.numeric(forecast(my_mod)$mean)
    pred_dc_2a[k] <- sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:7])
     # modèles exponentiels
    # Méthode 2 : lissage exponentiel
    my_mod_exp <- ets(my_ts)
    forecast_my_mod_exp <- as.numeric(forecast(my_mod_exp)$mean)
    forecast_my_mod_exp <- ifelse(forecast_my_mod_exp > 0, forecast_my_mod_exp, 0)
    pred_dc_2b[k] <- round(sum(forecast_my_mod_exp[1:7]), 0)
    # Méthode 3 : lissage exponentiel sur données hebdomadaires
    temp <- my_basis[my_basis$dep == nom_dep[k] & !(my_basis$semaine %in% 
                                          c("semaine_t0-4", "semaine_t0-3", 
                                            "semaine_t0-2", "semaine_t0-1", "semaine_t00")), ]
    my_ts_exp <- zoo(temp$dc, temp$jour)
    my_mod_exp_2 <- ets(my_ts_exp)
    forecast_my_mod_exp <- as.numeric(forecast(my_mod_exp_2)$mean)
    forecast_my_mod_exp <- ifelse(forecast_my_mod_exp > 0, forecast_my_mod_exp, 0)
    pred_dc_2c[k] <- round(forecast_my_mod_exp[1], 0)
    
    
  }
}

On représente le graphique des valeurs prédites / valeurs observées :

par(mfrow = c(1, 3))
plot(pred_dc_2a, my_basis_dc[my_basis_dc$semaine == "semaine_t00", "dc"],
     xlab = "valeurs prédites", ylab = "valeurs observées", main = "Box-Jenkins")
abline(a = 0, b = 1)
text(pred_dc_2a, my_basis_dc[my_basis_dc$semaine == "semaine_t00", "dc"], 
     my_basis_dc[my_basis_dc$semaine == "semaine_t00", "dep"], pos = 2)
plot(pred_dc_2b, my_basis_dc[my_basis_dc$semaine == "semaine_t00", "dc"],
     xlab = "valeurs prédites", ylab = "valeurs observées", main = "Lissage exponentiel journalier")
abline(a = 0, b = 1)
text(pred_dc_2b, my_basis_dc[my_basis_dc$semaine == "semaine_t00", "dc"], 
     my_basis_dc[my_basis_dc$semaine == "semaine_t00", "dep"], pos = 2)
plot(pred_dc_2c, my_basis_dc[my_basis_dc$semaine == "semaine_t00", "dc"],
     xlab = "valeurs prédites", ylab = "valeurs observées", main = "Lissage exponentiel hebdomadaire")
abline(a = 0, b = 1)
text(pred_dc_2c, my_basis_dc[my_basis_dc$semaine == "semaine_t00", "dc"], 
     my_basis_dc[my_basis_dc$semaine == "semaine_t00", "dep"], pos = 2)

L’écart quadratique moyen est égal ici à :

c(
  mean((pred_dc_2a - my_basis_dc[my_basis_dc$semaine == "semaine_t00", "dc"]) ^ 2, na.rm = T),
  mean((pred_dc_2b - my_basis_dc[my_basis_dc$semaine == "semaine_t00", "dc"]) ^ 2, na.rm = T),
  mean((pred_dc_2c - my_basis_dc[my_basis_dc$semaine == "semaine_t00", "dc"]) ^ 2, na.rm = T)
)

## [1] 91.94582 78.50495 63.25743

Les 3 prédictions sont très proches et on va choisir un algorithme de type stepwise sur les prédictions pour choisir la meilleure combinaison et ne garder qu’une prédiction de type série temporelle:

lm_2_dc_ts <- step(lm(my_basis[my_basis$semaine == "semaine_t00", "dc"] ~ 
                         pred_dc_2a + pred_dc_2b + pred_dc_2c - 1))

## Start:  AIC=402.88
## my_basis[my_basis$semaine == "semaine_t00", "dc"] ~ pred_dc_2a + 
##     pred_dc_2b + pred_dc_2c - 1
## 
##              Df Sum of Sq    RSS    AIC
## - pred_dc_2a  1      7.05 5145.9 401.01
## - pred_dc_2b  1      9.73 5148.5 401.07
## <none>                    5138.8 402.88
## - pred_dc_2c  1    653.22 5792.0 412.96
## 
## Step:  AIC=401.01
## my_basis[my_basis$semaine == "semaine_t00", "dc"] ~ pred_dc_2b + 
##     pred_dc_2c - 1
## 
##              Df Sum of Sq    RSS    AIC
## - pred_dc_2b  1      3.12 5149.0 399.07
## <none>                    5145.9 401.01
## - pred_dc_2c  1    681.64 5827.5 411.58
## 
## Step:  AIC=399.07
## my_basis[my_basis$semaine == "semaine_t00", "dc"] ~ pred_dc_2c - 
##     1
## 
##              Df Sum of Sq   RSS    AIC
## <none>                     5149 399.07
## - pred_dc_2c  1     66987 72136 663.69

pred_dc_2 <- predict(lm_2_dc_ts)
mean((pred_dc_2 - na.omit(my_basis[my_basis$semaine == "semaine_t00", "dc"])) ^ 2)

## [1] 50.98007

7.3 Combinaison des prédictions

Combinaison des prédictions: on peut envisager de faire un panaché des deux prédictions en régressant (avec un algorithme de type stepwise) le nombre de décés observé la semaine t0 en fonction des deux méthodes de régression. On obtient l’écart moyen quadratique suivant :

lm_dc_3 <- lm(my_basis_dc[my_basis_dc$semaine == "semaine_t00", "dc"] ~ 
                 pred_dc_1 + pred_dc_2 - 1)
mean((predict(lm_dc_3) - na.omit(my_basis_dc[my_basis_dc$semaine == "semaine_t00", "dc"])) ^ 2)

## [1] 37.44021

On adapte le poids des prédictions en fonction de la semaine à prédire

semaine_to_drop <- c("semaine_t0-4", "semaine_t0-3", "semaine_t0-2", "semaine_t0-1", "semaine_t00")
pred_dc_1_s2 <- pred_dc_1
pred_dc_2a_s2 <- pred_dc_2a
pred_dc_2b_s2 <- pred_dc_2b
pred_dc_2c_s2 <- pred_dc_2c

y_true <- my_basis[my_basis$semaine == "semaine_t00", "dc"]

for (j in 0:0) {
  
  semaine_to_estim <-  paste0("semaine_t0", j)
  y_true <- c(y_true, my_basis[my_basis$semaine == semaine_to_estim, "dc"])
  semaine_to_drop <- c(semaine_to_drop, paste0("semaine_t0", j + 1))
  res_lm_dc_1 <- lm(dc ~  region + rea:region - 1, 
             data = my_basis_dc[!(my_basis_dc$semaine %in% semaine_to_drop), ])
  pred_dc_1_s2 <- c(pred_dc_1_s2, 
     round(predict(res_lm_dc_1, newdata = my_basis_dc[my_basis_dc$semaine == semaine_to_estim, ])))
  pred_dc_2a_temp <- numeric(length(nom_dep))
  pred_dc_2b_temp <- numeric(length(nom_dep))
  pred_dc_2c_temp <- numeric(length(nom_dep))

  for (k in 1:length(nom_dep)) {
    temp <- hospital[!(hospital$semaine %in% semaine_to_drop) & 
                     hospital$dep == nom_dep[k], ]
    my_ts <- zoo(temp$incid_dc, temp$jour)
    my_ts_diff <- diff(my_ts)
    # tseries::adf.test(my_ts) 
    # tseries::adf.test(my_ts_diff)
    if (nom_dep[k] %in% c("975", "977", "978")) {
      pred_dc_2[k] <- NA
    } else {
      my_mod <- forecast::auto.arima(my_ts_diff)
      forecast_my_mod <- as.numeric(forecast(my_mod, h = 14)$mean)
      temp <- sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:7])
      pred_dc_2a_temp[k] <- sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:14]) - temp
      # modèles exponentiels
      # Méthode 2 : lissage exponentiel
      my_mod_exp <- ets(my_ts)
      forecast_my_mod_exp <- as.numeric(forecast(my_mod_exp, h = 14)$mean)
      forecast_my_mod_exp <- ifelse(forecast_my_mod_exp > 0, forecast_my_mod_exp, 0)
      temp <- round(sum(forecast_my_mod_exp[1:7]), 0)
      pred_dc_2b_temp[k] <- round(sum(forecast_my_mod_exp[1:14]), 0) - temp
      # Méthode 3 : lissage exponentiel sur données hebdomadaires
      temp <- my_basis[my_basis$dep == nom_dep[k] & !(my_basis$semaine %in% semaine_to_drop), ]
      my_ts_exp <- zoo(temp$dc, temp$jour)
      if (all(my_ts_exp == 0)) {
        pred_dc_2c_temp[k] <- 0
      } else {
        my_mod_exp_2 <- ets(my_ts_exp)
        forecast_my_mod_exp <- as.numeric(forecast(my_mod_exp_2)$mean)
        forecast_my_mod_exp <- ifelse(forecast_my_mod_exp > 0, forecast_my_mod_exp, 0)
        pred_dc_2c_temp[k] <- round(forecast_my_mod_exp[2], 0)
      }
    }
    
  }
   pred_dc_2a_s2 <- c(pred_dc_2a_s2, pred_dc_2a_temp)
   pred_dc_2b_s2 <- c(pred_dc_2b_s2, pred_dc_2b_temp)
   pred_dc_2c_s2 <- c(pred_dc_2c_s2, pred_dc_2c_temp)
}


lm_2_dc_ts_s1 <- step(lm(y_true ~ pred_dc_2a_s2 + pred_dc_2b_s2 + pred_dc_2c_s2 - 1))

## Start:  AIC=819.05
## y_true ~ pred_dc_2a_s2 + pred_dc_2b_s2 + pred_dc_2c_s2 - 1
## 
##                 Df Sum of Sq   RSS    AIC
## - pred_dc_2b_s2  1      0.08 11308 817.05
## <none>                       11308 819.05
## - pred_dc_2a_s2  1    143.97 11452 819.61
## - pred_dc_2c_s2  1    783.26 12091 830.58
## 
## Step:  AIC=817.05
## y_true ~ pred_dc_2a_s2 + pred_dc_2c_s2 - 1
## 
##                 Df Sum of Sq   RSS    AIC
## <none>                       11308 817.05
## - pred_dc_2a_s2  1    288.79 11597 820.15
## - pred_dc_2c_s2  1    893.33 12202 830.41

pred_dc_2_s2 <- predict(lm_2_dc_ts_s1)

lm_dc_3b <- lm(y_true ~ pred_dc_1_s2 + pred_dc_2_s2 - 1)

#######
# Semaine + 2
#######

semaine_to_drop <- c("semaine_t0-4", "semaine_t0-3", "semaine_t0-2", "semaine_t0-1", "semaine_t00", "semaine_t01")
pred_dc_1_s3 <- pred_dc_1_s2
pred_dc_2a_s3 <- pred_dc_2a_s2
pred_dc_2b_s3 <- pred_dc_2b_s2
pred_dc_2c_s3 <- pred_dc_2c_s2


for (j in 0:0) {
  
  semaine_to_estim <-  paste0("semaine_t0", j)
  y_true <- c(y_true, my_basis[my_basis$semaine == semaine_to_estim, "dc"])
  semaine_to_drop <- c(semaine_to_drop, paste0("semaine_t0", j + 2))
  
  res_lm_dc_1 <- lm(dc ~  region + rea:region - 1, 
             data = my_basis_dc[!(my_basis_dc$semaine %in% semaine_to_drop), ])
  pred_dc_1_s3 <- c(pred_dc_1_s3, round(predict(res_lm_dc_1, 
                      newdata = my_basis_dc[my_basis_dc$semaine == semaine_to_estim, ])))
  
  pred_dc_2a_temp <- numeric(length(nom_dep))
  pred_dc_2b_temp <- numeric(length(nom_dep))
  pred_dc_2c_temp <- numeric(length(nom_dep))

  for (k in 1:length(nom_dep)) {
     temp <- hospital[!(hospital$semaine %in% semaine_to_drop) & hospital$dep == nom_dep[k], ]
     my_ts <- zoo(temp$incid_dc, temp$jour)
     my_ts_diff <- diff(my_ts)
     # tseries::adf.test(my_ts) 
     # tseries::adf.test(my_ts_diff)
     if (nom_dep[k] %in% c("975", "977", "978")) {
       pred_dc_2[k] <- NA
     } else {
       my_mod <- forecast::auto.arima(my_ts_diff)
       forecast_my_mod <- as.numeric(forecast(my_mod, h = 21)$mean)
       temp1 <- sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:7])
       temp2 <- sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:14]) - temp1
       temp3 <- sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:21]) - temp1 - temp2
       pred_dc_2a_temp[k] <- ifelse(temp3 > 0, round(temp3), 0)
       # modèles exponentiels
       # Méthode 2 : lissage exponentiel
       my_mod_exp <- ets(my_ts)
       forecast_my_mod_exp <- as.numeric(forecast(my_mod_exp, h = 21)$mean)
       forecast_my_mod_exp <- ifelse(forecast_my_mod_exp > 0, forecast_my_mod_exp, 0)
       temp1 <- round(sum(forecast_my_mod_exp[1:7]), 0)
       temp2 <- round(sum(forecast_my_mod_exp[1:14]), 0) - temp1
       pred_dc_2b_temp[k] <- round(sum(forecast_my_mod_exp[1:21]), 0) - temp2 - temp1
       # Méthode 3 : lissage exponentiel sur données hebdomadaires
       temp <- my_basis[my_basis$dep == nom_dep[k] & !(my_basis$semaine %in% semaine_to_drop), ]
       my_ts_exp <- zoo(temp$dc, temp$jour)
       if (all(my_ts_exp == 0)) {
         pred_dc_2c_temp[k] <- 0
       } else {
         my_mod_exp_2 <- ets(my_ts_exp)
         forecast_my_mod_exp <- as.numeric(forecast(my_mod_exp_2)$mean)
         forecast_my_mod_exp <- ifelse(forecast_my_mod_exp > 0, forecast_my_mod_exp, 0)
         pred_dc_2c_temp[k] <- round(forecast_my_mod_exp[3], 0)
       }
    }
}

  pred_dc_2a_s3 <- c(pred_dc_2a_s3, pred_dc_2a_temp)
  pred_dc_2b_s3 <- c(pred_dc_2b_s3, pred_dc_2b_temp)
  pred_dc_2c_s3 <- c(pred_dc_2c_s3, pred_dc_2c_temp)
}

lm_2_dc_ts_s2 <- step(lm(y_true ~ pred_dc_2a_s3 + pred_dc_2b_s3 + pred_dc_2c_s3 - 1))

## Start:  AIC=1268.86
## y_true ~ pred_dc_2a_s3 + pred_dc_2b_s3 + pred_dc_2c_s3 - 1
## 
##                 Df Sum of Sq   RSS    AIC
## - pred_dc_2b_s3  1     14.75 19581 1267.1
## <none>                       19567 1268.9
## - pred_dc_2c_s3  1    223.36 19790 1270.3
## - pred_dc_2a_s3  1   1176.42 20743 1284.5
## 
## Step:  AIC=1267.09
## y_true ~ pred_dc_2a_s3 + pred_dc_2c_s3 - 1
## 
##                 Df Sum of Sq   RSS    AIC
## <none>                       19581 1267.1
## - pred_dc_2c_s3  1    208.62 19790 1268.3
## - pred_dc_2a_s3  1   2017.74 21599 1294.8

pred_dc_2_s3 <- predict(lm_2_dc_ts_s2)

lm_dc_3c <- lm(y_true ~ pred_dc_1_s3 + pred_dc_2_s3 - 1)

#######
# Semaine T + 3
#######

semaine_to_drop <- c("semaine_t0-4", "semaine_t0-3", "semaine_t0-2", "semaine_t0-1", 
                     "semaine_t00", "semaine_t01", "semaine_t02")
pred_dc_1_s4 <- pred_dc_1_s3
pred_dc_2a_s4 <- pred_dc_2a_s3
pred_dc_2b_s4 <- pred_dc_2b_s3
pred_dc_2c_s4 <- pred_dc_2c_s3


for (j in 0:0) {
  
  semaine_to_estim <-  paste0("semaine_t0", j)
  y_true <- c(y_true, my_basis[my_basis$semaine == semaine_to_estim, "dc"])
  semaine_to_drop <- c(semaine_to_drop, paste0("semaine_t0", j + 3))
  
  res_lm_dc_1 <- lm(dc ~  region + rea:region - 1, 
             data = my_basis_dc[!(my_basis_dc$semaine %in% semaine_to_drop), ])
  pred_dc_1_s4 <- c(pred_dc_1_s4, round(predict(res_lm_dc_1, 
                      newdata = my_basis_dc[my_basis_dc$semaine == semaine_to_estim, ])))
  
  pred_dc_2a_temp <- numeric(length(nom_dep))
  pred_dc_2b_temp <- numeric(length(nom_dep))
  pred_dc_2c_temp <- numeric(length(nom_dep))

  for (k in 1:length(nom_dep)) {
     temp <- hospital[!(hospital$semaine %in% semaine_to_drop) & hospital$dep == nom_dep[k], ]
     my_ts <- zoo(temp$incid_dc, temp$jour)
     my_ts_diff <- diff(my_ts)
     # tseries::adf.test(my_ts) 
     # tseries::adf.test(my_ts_diff)
     if (nom_dep[k] %in% c("975", "977", "978")) {
       pred_dc_2[k] <- NA
     } else {
       my_mod <- forecast::auto.arima(my_ts_diff)
       forecast_my_mod <- as.numeric(forecast(my_mod, h = 28)$mean)
       temp1 <- sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:7])
       temp2 <- sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:14]) - temp1
       temp3 <- sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:21]) - temp1 - temp2 
       temp4 <- sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:28]) - temp1 - temp2 - temp3
       pred_dc_2a_temp[k] <- ifelse(temp4 > 0, round(temp4), 0)
       # modèles exponentiels
       # Méthode 2 : lissage exponentiel
       my_mod_exp <- ets(my_ts)
       forecast_my_mod_exp <- as.numeric(forecast(my_mod_exp, h = 28)$mean)
       forecast_my_mod_exp <- ifelse(forecast_my_mod_exp > 0, forecast_my_mod_exp, 0)
       temp1 <- round(sum(forecast_my_mod_exp[1:7]), 0)
       temp2 <- round(sum(forecast_my_mod_exp[1:14]), 0) - temp1
       temp3 <- round(sum(forecast_my_mod_exp[1:21]), 0) - temp1 - temp2
       pred_dc_2b_temp[k] <- round(sum(forecast_my_mod_exp[1:28]), 0) - temp1 - temp2 - temp3
       # Méthode 3 : lissage exponentiel sur données hebdomadaires
       temp <- my_basis[my_basis$dep == nom_dep[k] & !(my_basis$semaine %in% semaine_to_drop), ]
       my_ts_exp <- zoo(temp$dc, temp$jour)
       if (all(my_ts_exp == 0)) {
         pred_dc_2c_temp[k] <- 0
       } else {
         my_mod_exp_2 <- ets(my_ts_exp)
         forecast_my_mod_exp <- as.numeric(forecast(my_mod_exp_2)$mean)
         forecast_my_mod_exp <- ifelse(forecast_my_mod_exp > 0, forecast_my_mod_exp, 0)
         pred_dc_2c_temp[k] <- round(forecast_my_mod_exp[4], 0)
       }
    }
}

  pred_dc_2a_s4 <- c(pred_dc_2a_s4, pred_dc_2a_temp)
  pred_dc_2b_s4 <- c(pred_dc_2b_s4, pred_dc_2b_temp)
  pred_dc_2c_s4 <- c(pred_dc_2c_s4, pred_dc_2c_temp)
}

lm_2_dc_ts_s3 <- step(lm(y_true ~ pred_dc_2a_s4 + pred_dc_2b_s4 + pred_dc_2c_s4 - 1))

## Start:  AIC=1733.99
## y_true ~ pred_dc_2a_s4 + pred_dc_2b_s4 + pred_dc_2c_s4 - 1
## 
##                 Df Sum of Sq   RSS    AIC
## - pred_dc_2b_s4  1      1.53 29105 1732.0
## <none>                       29104 1734.0
## - pred_dc_2c_s4  1    295.57 29399 1736.1
## - pred_dc_2a_s4  1   1360.98 30465 1750.5
## 
## Step:  AIC=1732.01
## y_true ~ pred_dc_2a_s4 + pred_dc_2c_s4 - 1
## 
##                 Df Sum of Sq   RSS    AIC
## <none>                       29105 1732.0
## - pred_dc_2c_s4  1     299.7 29405 1734.2
## - pred_dc_2a_s4  1    2346.0 31451 1761.3

pred_dc_2_s4 <- predict(lm_2_dc_ts_s3)

lm_dc_4c <- lm(y_true ~ pred_dc_1_s4 + pred_dc_2_s4 - 1)

7.4 Prédiction

On prédit:

• le nombre de décès à venir du [26 février 2021; 04 mars 2021] en utilisant les nouvelles réanimations du [19 février 2021; 25 février 2021]

• le nombre de décès à venir du [05 mars 2021; 11 mars 2021] en utilisant la prédiction des réanimations à venir du [26 février 2021; 04 mars 2021]

• le nombre de décès à venir du [12 mars 2021; 18 mars 2021] en utilisant la prédiction des réanimations à venir du [05 mars 2021; 11 mars 2021]

• le nombre de décès à venir du [19 mars 2021; 25 mars 2021] en utilisant la prédiction des réanimations à venir du [05 mars 2021; 11 mars 2021]

Pour cela, on actualise le modèle, c’est-à-dire qu’on inclut la dernière semaine observée:

res_lm <- lm(dc ~  region + rea:region - 1, 
             data = my_basis_dc[!(my_basis_dc$semaine %in% c("semaine_t0-2", "semaine_t0-1")), ])

# semaine t+1
new_data_dc_1 <- my_basis_dc[my_basis_dc$semaine %in% c("semaine_t0-1", "semaine_t0-2", "semaine_t0-3", "semaine_t0-4"),  ]
pred_dc_1 <- predict(res_lm, newdata = new_data_dc_1)

pred_dc_2 <- matrix(0, length(nom_dep), 4)
pred_dc_2a <- matrix(0, length(nom_dep), 4)
pred_dc_2b <- matrix(0, length(nom_dep), 4)
pred_dc_2c <- matrix(0, length(nom_dep), 4)
for (k in 1:length(nom_dep)) {
  temp <- hospital[!(hospital$semaine %in% c("semaine_t0-4", "semaine_t0-3", "semaine_t0-2", "semaine_t0-1")) & 
                     hospital$dep == nom_dep[k], ]
  my_ts <- zoo(temp$incid_dc, temp$jour)
  my_ts_diff <- diff(my_ts)
  # tseries::adf.test(my_ts) 
  # tseries::adf.test(my_ts_diff)
  if (nom_dep[k] %in% c("975", "977", "978")) {
    pred_rea_2[k] <- NA
  } else {
    my_mod <- forecast::auto.arima(my_ts_diff)
    forecast_my_mod <- as.numeric(forecast(my_mod, h = 28)$mean)
    pred_3a_s1 <- sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:7])
    pred_3a_s2 <- sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:14]) - pred_3a_s1
    pred_3a_s3 <- sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:21]) - 
      pred_3a_s1 - pred_3a_s2
    pred_3a_s4 <- sum((as.numeric(my_ts[length(my_ts)]) + cumsum(forecast_my_mod))[1:28]) - 
      pred_3a_s1 - pred_3a_s2 - pred_3a_s3
        # Lissage exponentiel
    my_mod_exp <- ets(my_ts)
    forecast_my_mod_exp <- as.numeric(forecast(my_mod_exp, h = 28)$mean)
    forecast_my_mod_exp <- ifelse(forecast_my_mod_exp > 0, forecast_my_mod_exp, 0)
    pred_3b_s1 <- round(sum(forecast_my_mod_exp[1:7]), 0)
    pred_3b_s2 <- round(sum(forecast_my_mod_exp[1:14]), 0) - pred_3b_s1
    pred_3b_s3 <- round(sum(forecast_my_mod_exp[1:21]), 0) - pred_3b_s2 - pred_3b_s1
    pred_3b_s4 <- round(sum(forecast_my_mod_exp[1:28]), 0) - pred_3b_s3 - pred_3b_s2 - pred_3b_s1
    # Méthode 3 : lissage exponentiel sur données hebdomadaires
    temp <- my_basis[my_basis$dep == nom_dep[k] & !(my_basis$semaine %in% 
                                          c("semaine_t0-4", "semaine_t0-3", "semaine_t0-2", "semaine_t0-1")), ]
    my_ts_exp <- zoo(temp$dc, temp$jour)
    my_mod_exp_2 <- ets(my_ts_exp)
    forecast_my_mod_exp <- as.numeric(forecast(my_mod_exp_2)$mean)
    forecast_my_mod_exp <- ifelse(forecast_my_mod_exp > 0, forecast_my_mod_exp, 0)
    pred_3c_s1 <- round(forecast_my_mod_exp[1], 0)
    pred_3c_s2 <- round(forecast_my_mod_exp[2], 0)
    pred_3c_s3 <- round(forecast_my_mod_exp[3], 0)    
    pred_3c_s4 <- round(forecast_my_mod_exp[4], 0) 
      
    pred_dc_2[k, 1] <- predict(lm_2_dc_ts, newdata = data.frame(pred_dc_2a = pred_3a_s1,
                                                 pred_dc_2b = pred_3b_s1,
                                                 pred_dc_2c = pred_3c_s1))
    pred_dc_2[k, 2] <- predict(lm_2_dc_ts_s1, newdata = data.frame(pred_dc_2a_s2 = pred_3a_s2,
                                                 pred_dc_2b_s2 = pred_3b_s2,
                                                 pred_dc_2c_s2 = pred_3c_s2))
    pred_dc_2[k, 3] <- predict(lm_2_dc_ts_s2, newdata = data.frame(pred_dc_2a_s3 = pred_3a_s3,
                                                 pred_dc_2b_s3 = pred_3b_s3,
                                                 pred_dc_2c_s3 = pred_3c_s3))
    pred_dc_2[k, 4] <- predict(lm_2_dc_ts_s3, newdata = data.frame(pred_dc_2a_s4 = pred_3a_s4,
                                                 pred_dc_2b_s4 = pred_3b_s4,
                                                 pred_dc_2c_s4 = pred_3c_s4))  
  }
}

n_4 <- 4 * length(nom_dep) 

pred_dc_a <- predict(lm_dc_3, newdata = data.frame(pred_dc_1 = 
                        pred_dc_1[new_data_dc_1$semaine == "semaine_t0-1"],
                        pred_dc_2 = as.vector(pred_dc_2)[1:(n_4 / 4)]))

pred_dc_b <- predict(lm_dc_3b, newdata = data.frame(
  pred_dc_1_s2 = pred_dc_1[new_data_dc_1$semaine == "semaine_t0-2"],
  pred_dc_2_s2 = as.vector(pred_dc_2)[((n_4 / 4) + 1):(2 * n_4 / 4)]))

pred_dc_c <- predict(lm_dc_3c, newdata = data.frame(
  pred_dc_1_s3 = pred_dc_1[new_data_dc_1$semaine == "semaine_t0-3"],
  pred_dc_2_s3 = as.vector(pred_dc_2)[(2 * n_4 / 4 + 1):(3 * n_4 / 4)]))

pred_dc_d <- predict(lm_dc_4c, newdata = data.frame(
  pred_dc_1_s4 = pred_dc_1[new_data_dc_1$semaine == "semaine_t0-4"],
  pred_dc_2_s4 = as.vector(pred_dc_2)[(3 * n_4 / 4 + 1):n_4]))



# on synthétise les résultats
new_data <- my_basis[my_basis$semaine %in% "semaine_t0-1", ]
new_data$this_week <- my_basis_dc[my_basis_dc$semaine == "semaine_t00", "dc"]
new_data$next_week <- pred_dc_a
new_data$next_two_week <- pred_dc_b
new_data$next_three_week <- pred_dc_c
new_data$next_four_week <- pred_dc_d
my_basis[my_basis$semaine %in% "semaine_t0-1", "dc"] <- pred_dc_a
my_basis[my_basis$semaine %in% "semaine_t0-2", "dc"] <- pred_dc_b
my_basis[my_basis$semaine %in% "semaine_t0-3", "dc"] <- pred_dc_c
my_basis[my_basis$semaine %in% "semaine_t0-4", "dc"] <- pred_dc_d

On va représenter l’évolution du nombre de décès dans un intervalle de temps de 5 semaines :

• les 7 derniers jours passés : [19 février 2021; 25 février 2021]
• la semaine à venir : [26 février 2021; 04 mars 2021]
• la 2ème semaine à venir : [05 mars 2021; 11 mars 2021]
• la 3ème semaine à venir : [12 mars 2021; 18 mars 2021]
• la 4ème semaine à venir : [12 mars 2021; 18 mars 2021]

new_data_long <- tidyr::pivot_longer(data = select(new_data, dep, region, 
                                    this_week, next_week, next_two_week, next_three_week, next_four_week),
                                   col = 3:7,
                                   names_to = "semaine",
                                   values_to = "dc")
new_data_long$semaine <- factor(new_data_long$semaine,
      levels = c("this_week", "next_week", "next_two_week", "next_three_week", "next_four_week"),
      labels = c(paste0("[", format(to_day - 7, '%d %b'), "; ",  
                        format(to_day - 1, '%d %b'), "]"),
                 paste0("[", format(to_day, '%d %b'), "; ",  
                        format(to_day + 6, '%d %b'), "]"),
                 paste0("[", format(to_day + 7, '%d %b'), "; ",  
                        format(to_day + 13, '%d %b'), "]"),
                 paste0("[", format(to_day + 14, '%d %b'), "; ",  
                        format(to_day + 20, '%d %b'), "]"), 
                 paste0("[", format(to_day + 21, '%d %b'), "; ",  
                        format(to_day + 27, '%d %b'), "]")
                 )
      )

new_data_long$region <- factor(new_data_long$region, levels = hosp_region$region)
p <- ggplot(new_data_long, aes(x = semaine, y = dc,  group = dep))+
    geom_line() +
  facet_wrap(~region)
plotly::ggplotly(p)

On aggrège les données à la France entière:

my_basis_fr <- my_basis %>%
  group_by(semaine, jour) %>%
  summarise(dc = sum(dc))
p <- ggplot(data = filter(my_basis_fr, semaine %in% 
                      c("semaine_t0-4", "semaine_t0-3", "semaine_t0-2", "semaine_t0-1", "semaine_t00")),
            aes(x = jour, y = dc)) +
  geom_line(col = "red") +
  geom_line(data = filter(my_basis_fr, !(semaine %in% 
                        c("semaine_t0-4", "semaine_t0-3", "semaine_t0-2", "semaine_t0-1"))), 
            aes(x = jour, y = dc)) +
  labs(title = "Prédiction des nouveaux décès dans les 28 jours",
       x = "semaine",
       y = "décès",
       fill = "Age") 
plotly::ggplotly(p)

Soit un nombre de décès par jour de :

new_data_long %>%
  group_by(semaine) %>%
  summarize(dc = sum(dc, na.rm = T) / 7)

## # A tibble: 5 x 2
##   semaine                 dc
##   <fct>                <dbl>
## 1 [19 févr.; 25 févr.]  259.
## 2 [26 févr.; 04 mars]     0 
## 3 [05 mars; 11 mars]      0 
## 4 [12 mars; 18 mars]    256.
## 5 [19 mars; 25 mars]    247.