From 50c381db1056bccf38c37c9dfc41463bb51ed62f Mon Sep 17 00:00:00 2001 From: Helene31 Date: Thu, 23 Apr 2020 11:01:54 +0200 Subject: [PATCH] maj --- module3/exo3/ConcentrationCO2.Rmd | 151 +- module3/exo3/ConcentrationCO2.html | 209 +- module3/exo3/exercice_en.Rmd | 33 - module3/exo3/exercice_fr.Rmd | 33 - module3/exo3/weekly_in_situ_co2_mlo.csv | 3210 +++++++++++++++++++++++ 5 files changed, 3460 insertions(+), 176 deletions(-) delete mode 100644 module3/exo3/exercice_en.Rmd delete mode 100644 module3/exo3/exercice_fr.Rmd create mode 100644 module3/exo3/weekly_in_situ_co2_mlo.csv diff --git a/module3/exo3/ConcentrationCO2.Rmd b/module3/exo3/ConcentrationCO2.Rmd index 4c254d9..d07e2e5 100644 --- a/module3/exo3/ConcentrationCO2.Rmd +++ b/module3/exo3/ConcentrationCO2.Rmd @@ -10,7 +10,7 @@ output: html_document En 1958, Charles David Keeling a initié une mesure de la concentration de CO2 dans l'atmosphère à l'observatoire de Mauna Loa, Hawaii, États-Unis qui continue jusqu'à aujourd'hui. L'objectif initial était d'étudier la variation saisonnière, mais l'intérêt s'est déplacé plus tard vers l'étude de la tendance croissante dans le contexte du changement climatique. En honneur à Keeling, ce jeu de données est souvent appelé "Keeling Curve" (voir (https://en.wikipedia.org/wiki/Keeling_Curve) pour l'histoire et l'importance de ces données). -Les données sont disponibles sur le site Web de l'institut Scripps. Utilisez le fichier avec les observations hebdomadaires. Attention, ce fichier est mis à jour régulièrement avec de nouvelles observations. Notez donc bien la date du téléchargement, et gardez une copie locale de la version précise que vous analysez. Faites aussi attention aux données manquantes. +Les données sont disponibles sur le site Web de l' [Institut Scripps](https://scrippsco2.ucsd.edu/) . J'ai utilisé par erreur les observations mensuelles (je n'ai pas le temps de refaire tout le travail en utilisant les données hebdomadaires, ce sont d'ailleurs les données mensuelles qui sont utilisées en général dans les études d'impact climatiques ) [observations mensuelles](https://scrippsco2.ucsd.edu/assets/data/atmospheric/stations/in_situ_co2/monthly/monthly_in_situ_co2_mlo.csv). Attention, ce fichier est mis à jour régulièrement avec de nouvelles observations. Notez donc bien la date du téléchargement, et gardez une copie locale de la version précise que vous analysez. Faites aussi attention aux données manquantes. ### Pré-requis @@ -18,10 +18,18 @@ Traitement de suites chronologiques Quelques références: -- [caschrono: Séries Temporelles Avec R] (https://cran.r-project.org/web/packages/caschrono/) - Yves Aragon - Université Toulouse Capitole - 28 janvier 2019 +- [Introduction à l’Étude des Séries Temporelles](https://perso.math.univ-toulouse.fr/jydauxoi/files/2017/04/poly_eleves.pdf) J-Y. Dauxois 2016-2017 +- [ARIMA modelling in R](https://otexts.com/fpp2/arima-r.html) +- [Séries temporelles – Modèles ARIMA.](https://didierdelignieresblog.files.wordpress.com/2016/03/arimacomplet.pdf) +Didier Delignières Séminaire EA "Sport – Performance – Santé" Mars 2000 +- [Introduction à la manipulation de série temporelle avec R MAP-STA2 : Séries chronologiques](https://www.imo.universite-paris-saclay.fr/~goude/Materials/time_series/cours1_R_serie_temp.pdf) Yannig Goude yannig.goude@edf.fr 2019-2020 +- [Séries temporelles, avec R](http://avram.perso.univ-pau.fr/proc/geo3.pdf) Florin Avram +(https://github.com/Peymankor/Data-Science_Portfolio/blob/master/Time%20Series%20Analysis-Historical%20Co2/medium_post.Rmd) + +### Pré-traitements sur les données -### Create dataframe and load R libraries required for the different statistical treatments +Extrait des métadonnées dans le header du fichier csv téléchargé. The data file below contains 10 columns. @@ -35,9 +43,13 @@ The data file below contains 10 columns. Missing values are denoted by -99.99 - CO2 concentrations are measured on the '08A' calibration scale +CO2 concentrations are measured on the '08A' calibration scale + +**Chargement des librairies R, du fichier de données, renommage des colonnes, premières statistiques** -```{r } +```{r, message=FALSE, warning=FALSE} + +setwd("C:/Users/hraynal/EspaceTravailBadet/FORMATION_PERSO/2020-Reproductibilite/mooc-rr/module3/exo3") library(tidyverse) library(forecast) library(lubridate) @@ -55,18 +67,17 @@ dataCO2$Date <- ymd(paste0(dataCO2$Year, " ", dataCO2$Month, " ", "15")) ``` -** Remplacement dans la série des valeurs observées, des valeurs manquantes -99.99 par celles qui sont interpolées -** on enlève ensuite les observations manquantes -```{r } - +**Traitement des valeurs manquantes notées -99.99** +Il s'avère que dans la série des valeurs observées complétée par les valeurs interpolées, il reste des observations avec des valeurs manquantes (-99.99). On supprime ces observations. +```{r, message=FALSE, warning=FALSE } dataCO2 <- dataCO2[dataCO2$ObsCO2Comp != "-99.99", ] ``` -** Create a column Date with format YYYY MM DD -```{r } +**Création d'une variable date au format YYYY MM DD** +```{r , message=FALSE, warning=FALSE} dataCO2$Date <- ymd(paste0(dataCO2$Year, "-", dataCO2$Month, "-", "15")) @@ -74,9 +85,9 @@ dataCO2$Date <- ymd(paste0(dataCO2$Year, "-", dataCO2$Month, "-", "15")) ``` -### Représentation des résultats +### Représentations graphiques des résultats -```{r } +```{r, message=FALSE, warning=FALSE } ggplot(dataCO2,aes(Date, dataCO2$ObsCO2Comp)) + geom_line(color='orange') + xlab("Year, Month") + @@ -87,47 +98,127 @@ ggplot(dataCO2,aes(Date, dataCO2$ObsCO2Comp)) + scale_y_continuous() + theme(axis.text.y = element_text(face = "bold", color = "#993333", size = 10, hjust = 1),axis.title.y = element_text(size = 10)) + - ggtitle("Graphique 1") + ggtitle("Graphique 1: Evolution au cours du temps de la teneur en CO2") ``` -```{r } +```{r, message=FALSE, warning=FALSE } - library(viridis) dataCO2_by_year <- dataCO2 %>% group_by("Year") ggplot(dataCO2_by_year, aes(dataCO2_by_year$Month,dataCO2_by_year$ObsCO2Comp )) + geom_line(aes( group = dataCO2_by_year$Year , colour=dataCO2_by_year$Year)) + xlab("Month")+ ylab("CO2 Concentration (ppm)") + - ggtitle("Graphique saisonnier") + ggtitle("Graphique 2: Evolution saisonnière de la concentration en CO2, par année") ``` +- On déduit du graphique 1 que la série n'est pas stationnaire, elle présente une **tendance** (augmentation du taux de CO2 au cours du temps). +- La série montre une **composante saisonnière**, qui semble suivre le cycle annuel, comme en témoigne le graphique 2. En effet les courbes annuelles ont la même forme, tout en étant décalée dans le temps. +- On ne voit pas sur ces graphiques de ruptures dans le comportement de la série. + +- On ne détecte pas d'observations aberrantes. + +**Question 1: Réalisez un graphique qui vous montrera une oscillation périodique superposée à une évolution systématique plus lente.** +```{r, message=FALSE, warning=FALSE } +# Définition en tant que série temporelle +Co2_train <- ts(dataCO2$ObsCO2Comp, start = c(1958,3), frequency = 12) +T <- time(Co2_train) +base <- data.frame(Y=dataCO2$ObsCO2Comp,X1=as.numeric(T)) + +#essai d'ajustement à un modèle de régression linéaire +reg1 <- lm(Y~X1,data=base) +tendance1 <-predict(reg1) +T <-as.numeric(T) + +#Calcul des moyennes annuelles de teneur en CO2 +# <- cbind( levels(factor(dataCO2$Year)), tapply(dataCO2$ObsCO2Comp, dataCO2$Year, mean)) + +MeanCO2 <- tapply(dataCO2$ObsCO2Comp, dataCO2$Year, mean) + +tmp <- ymd(paste0(unique(dataCO2$Year), "-06-15")) +MeanCO2Year <- data.frame(tmp , as.numeric(MeanCO2) ) +colnames(MeanCO2Year) <- c("Year", "MeanCO2") +dataCO2M <- merge( dataCO2, MeanCO2Year, by="Year") + + + +ggplot() + + geom_line(aes( x=dataCO2$Date, y=dataCO2$ObsCO2Comp), color='orange') + + geom_line(aes(x=MeanCO2Year$Year, y=MeanCO2Year$MeanCO2 ), color="blue") + + geom_line(aes(x=dataCO2$Date, y=tendance1 ), color="grey") + + #geom_line(aes(x=T, y=tendance1 ), color="grey") + + xlab("Year, Month") + + scale_x_date(date_labels = "%Y-%m", date_breaks = "5 year") + + theme(axis.text.x = element_text(face = "bold", color = "#993333", + size = 12, angle = 45, hjust = 1)) + + ylab("CO2 Concentration (ppm)") + + scale_y_continuous() + + theme(axis.text.y = element_text(face = "bold", color = "#993333", + size = 10, hjust = 1),axis.title.y = element_text(size = 10)) + + ggtitle("Graphique 1: Evolution au cours du temps de la teneur en CO2") -### Modélisation -** Doc -(https://github.com/Peymankor/Data-Science_Portfolio/blob/master/Time%20Series%20Analysis-Historical%20Co2/medium_post.Rmd) -Série n'est pas stationnaire comme le montre le graphique +``` + + +### Modélisation de la série temporelle + + + +On va chercher à modéliser la série en utilisant une catégorie de modèles qui cherche à déterminer chaque valeur de la série en fonction des valeurs qui la précède (yt = f(yt-1, yt-2, …)). C'est le cas des modèles ARIMA ("AutoRegressive – Integrated – Moving Average"). Cette catégorie de modèles a été popularisée et formalisée par Box et Jenkins (1976). -Série montre une saisonnalité voir graphique 2 +Les processus autorégressifs supposent que chaque point peut être prédit par la somme pondérée d'un ensemble de points précédents, plus un terme aléatoire d'erreur. -Now, knowing the the non-statinary and seasonality of the data, it suggest to use theseasons differencing to model the data. To answer, +Le processus d'intégration suppose que chaque point présente une différence constante avec le point précédent. +Les processus de moyenne mobile supposent que chaque point est fonction des erreurs +entachant les points précédant, plus sa propre erreur. -* How is Autocorelation function and Partial Auto corellation? +Un modèle ARIMA est étiqueté comme modèle ARIMA (p,d,q), dans lequel: -Here is the plot of ACF and PACF from the *forecast* package: +- p est le nombre de termes auto-régressifs +- d est le nombre de différences +- q est le nombre de moyennes mobiles. + + +On va utiliser la fonction **auto.arima()** qui est un algorithme automatique qui permet de trouver le modèle ARIMA qui estime le mieux la série temporelle. -```{r} -Co2_train <- ts(dataCO2_by_year$ObsCO2Comp, start = c(1958,3), frequency = 12) + +```{r, message=FALSE, warning=FALSE} +Co2_train <- ts(dataCO2$ObsCO2Comp, start = c(1958,3), frequency = 12) Co2_train %>% ggtsdisplay() ``` +```{r, message=FALSE, warning=FALSE} + +auto.arima(Co2_train) +``` + + + + +En se basant sur le résultat de l'analyse précédente, on retient le modèle $ARIMA(1,1,1)(2,1,2)[12]$. On peut ensuite vérifier que les résidus ressemblent à un bruit blanc ou non. + + + +```{r, message=FALSE, warning=FALSE} +(fit_minaicc <- Arima(Co2_train, order=c(1,1,1),seasonal=list(order=c(2,1,2),period=12), + lambda = "auto" + )) +checkresiduals(fit_minaicc, lag=36) +fit_minaicc$aicc +``` + + +Les graphiques précédents montre que le résidu ressemble suffisamment au bruit blanc, que la valeur p est élevée et que le modèle a passé le test de la Ljong-Box. + + +```{r, message=FALSE, warning=FALSE} +autoplot(forecast(fit_minaicc, h=200)) +``` + -```{r} -Co2_train %>% diff(lag=12) %>% diff() %>% ggtsdisplay() -``` \ No newline at end of file diff --git a/module3/exo3/ConcentrationCO2.html b/module3/exo3/ConcentrationCO2.html index d221aef..b682fec 100644 --- a/module3/exo3/ConcentrationCO2.html +++ b/module3/exo3/ConcentrationCO2.html @@ -385,18 +385,24 @@ summary {

Sujet

En 1958, Charles David Keeling a initié une mesure de la concentration de CO2 dans l’atmosphère à l’observatoire de Mauna Loa, Hawaii, États-Unis qui continue jusqu’à aujourd’hui. L’objectif initial était d’étudier la variation saisonnière, mais l’intérêt s’est déplacé plus tard vers l’étude de la tendance croissante dans le contexte du changement climatique. En honneur à Keeling, ce jeu de données est souvent appelé “Keeling Curve” (voir (https://en.wikipedia.org/wiki/Keeling_Curve) pour l’histoire et l’importance de ces données).

-

Les données sont disponibles sur le site Web de l’institut Scripps. Utilisez le fichier avec les observations hebdomadaires. Attention, ce fichier est mis à jour régulièrement avec de nouvelles observations. Notez donc bien la date du téléchargement, et gardez une copie locale de la version précise que vous analysez. Faites aussi attention aux données manquantes.

+

Les données sont disponibles sur le site Web de l’ Institut Scripps . J’ai utilisé par erreur les observations mensuelles (je n’ai pas le temps de refaire tout le travail en utilisant les données hebdomadaires, ce sont d’ailleurs les données mensuelles qui sont utilisées en général dans les études d’impact climatiques ) observations mensuelles. Attention, ce fichier est mis à jour régulièrement avec de nouvelles observations. Notez donc bien la date du téléchargement, et gardez une copie locale de la version précise que vous analysez. Faites aussi attention aux données manquantes.

Pré-requis

Traitement de suites chronologiques

Quelques références:

+

(https://github.com/Peymankor/Data-Science_Portfolio/blob/master/Time%20Series%20Analysis-Historical%20Co2/medium_post.Rmd)

-
-

Create dataframe and load R libraries required for the different statistical treatments

+
+

Pré-traitements sur les données

+

Extrait des métadonnées dans le header du fichier csv téléchargé.

The data file below contains 10 columns.

  • Columns 1-4 give the dates in several redundant formats.
    • @@ -414,63 +420,17 @@ summary {

Missing values are denoted by -99.99

CO2 concentrations are measured on the ‘08A’ calibration scale

-
library(tidyverse)
-
## Warning: package 'tidyverse' was built under R version 3.5.3
-
## -- Attaching packages -------------------------------------------------------------------------------------------------------------- tidyverse 1.2.1 --
-
## v ggplot2 3.1.0       v purrr   0.3.2  
-## v tibble  2.1.1       v dplyr   0.8.0.1
-## v tidyr   0.8.3       v stringr 1.4.0  
-## v readr   1.3.1       v forcats 0.4.0
-
## Warning: package 'tibble' was built under R version 3.5.3
-
## Warning: package 'tidyr' was built under R version 3.5.3
-
## Warning: package 'readr' was built under R version 3.5.3
-
## Warning: package 'purrr' was built under R version 3.5.3
-
## Warning: package 'dplyr' was built under R version 3.5.3
-
## Warning: package 'stringr' was built under R version 3.5.3
-
## Warning: package 'forcats' was built under R version 3.5.3
-
## -- Conflicts ----------------------------------------------------------------------------------------------------------------- tidyverse_conflicts() --
-## x dplyr::filter() masks stats::filter()
-## x dplyr::lag()    masks stats::lag()
-
library(forecast)
-
## Warning: package 'forecast' was built under R version 3.5.3
-
library(lubridate)
-
## Warning: package 'lubridate' was built under R version 3.5.3
-
## 
-## Attaching package: 'lubridate'
-
## The following object is masked from 'package:base':
-## 
-##     date
-
library(car)
-
## Warning: package 'car' was built under R version 3.5.3
-
## Loading required package: carData
-
## Warning: package 'carData' was built under R version 3.5.2
-
## 
-## Attaching package: 'car'
-
## The following object is masked from 'package:dplyr':
-## 
-##     recode
-
## The following object is masked from 'package:purrr':
-## 
-##     some
-
library(scales)
-
## 
-## Attaching package: 'scales'
-
## The following object is masked from 'package:purrr':
-## 
-##     discard
-
## The following object is masked from 'package:readr':
-## 
-##     col_factor
-
library(patchwork)
-
## Warning: package 'patchwork' was built under R version 3.5.3
-
library(kableExtra)
-
## Warning: package 'kableExtra' was built under R version 3.5.3
-
## 
-## Attaching package: 'kableExtra'
-
## The following object is masked from 'package:dplyr':
-## 
-##     group_rows
-
dataCO2 <- read.csv("monthly_in_situ_co2_mlo.csv", sep="," ,skip = 57)
+
Chargement des librairies R, du fichier de données, renommage des colonnes, premières statistiques

+
setwd("C:/Users/hraynal/EspaceTravailBadet/FORMATION_PERSO/2020-Reproductibilite/mooc-rr/module3/exo3")
+library(tidyverse)
+library(forecast)
+library(lubridate)
+library(car)
+library(scales)
+library(patchwork)
+library(kableExtra)
+
+dataCO2 <- read.csv("monthly_in_situ_co2_mlo.csv", sep="," ,skip = 57)
 colnames(dataCO2) <- c("Year", "Month","Date1", "Date2", "ObsCO2", "SeasAdjCO2","SplineAdjCO2", "SplineAdjCO2Trend", "ObsCO2Comp", "SeasAdjCO2Comp")
 summary(dataCO2)

 
##       Year          Month            Date1           Date2     
@@ -495,13 +455,14 @@ summary(dataCO2)

 ##  3rd Qu.:377.55   3rd Qu.:377.35  
 ##  Max.   :414.83   Max.   :413.33
dataCO2$Date <- ymd(paste0(dataCO2$Year, " ", dataCO2$Month, " ", "15"))
-

** Remplacement dans la série des valeurs observées, des valeurs manquantes -99.99 par celles qui sont interpolées ** on enlève ensuite les observations manquantes

+

Traitement des valeurs manquantes notées -99.99

+

Il s’avère que dans la série des valeurs observées complétée par les valeurs interpolées, il reste des observations avec des valeurs manquantes (-99.99). On supprime ces observations.

dataCO2 <- dataCO2[dataCO2$ObsCO2Comp != "-99.99", ]
-

** Create a column Date with format YYYY MM DD

+

Création d’une variable date au format YYYY MM DD

dataCO2$Date <- ymd(paste0(dataCO2$Year, "-", dataCO2$Month, "-", "15"))
-
-

Représentation des résultats

+
+

Représentations graphiques des résultats

ggplot(dataCO2,aes(Date, dataCO2$ObsCO2Comp)) +
     geom_line(color='orange') +
     xlab("Year, Month") +
@@ -512,27 +473,115 @@ summary(dataCO2)
scale_y_continuous() + theme(axis.text.y = element_text(face = "bold", color = "#993333", size = 10, hjust = 1),axis.title.y = element_text(size = 10)) + - ggtitle("Graphique 1") -

-
 library(viridis)
-
## Loading required package: viridisLite
-
## 
-## Attaching package: 'viridis'
-
## The following object is masked from 'package:scales':
-## 
-##     viridis_pal
+ ggtitle("Graphique 1: Evolution au cours du temps de la teneur en CO2") +

dataCO2_by_year <- dataCO2 %>% group_by("Year")
 ggplot(dataCO2_by_year, aes(dataCO2_by_year$Month,dataCO2_by_year$ObsCO2Comp )) +
          geom_line(aes( group = dataCO2_by_year$Year , colour=dataCO2_by_year$Year)) +
          xlab("Month")+
          ylab("CO2 Concentration (ppm)") +
-         ggtitle("Graphique saisonnier")
-

+ ggtitle("Graphique 2: Evolution saisonnière de la concentration en CO2, par année") +

- On déduit du graphique 1 que la série n’est pas stationnaire, elle présente une tendance (augmentation du taux de CO2 au cours du temps).

+
    +

  • La série montre une composante saisonnière, qui semble suivre le cycle annuel, comme en témoigne le graphique 2. En effet les courbes annuelles ont la même forme, tout en étant décalée dans le temps.

    • +

  • On ne voit pas sur ces graphiques de ruptures dans le comportement de la série.

    • +

  • On ne détecte pas d’observations aberrantes.

    • +
+

Question 1: Réalisez un graphique qui vous montrera une oscillation périodique superposée à une évolution systématique plus lente.

+
# Définition en tant que série temporelle
+Co2_train <- ts(dataCO2$ObsCO2Comp, start = c(1958,3), frequency = 12)
+T <- time(Co2_train)
+base <- data.frame(Y=dataCO2$ObsCO2Comp,X1=as.numeric(T))
+
+#essai d'ajustement à un modèle de régression linéaire
+reg1 <- lm(Y~X1,data=base)
+tendance1 <-predict(reg1)
+T <-as.numeric(T)
+
+#Calcul des moyennes annuelles de teneur en CO2
+# <- cbind(  levels(factor(dataCO2$Year)),  tapply(dataCO2$ObsCO2Comp, dataCO2$Year, mean)) 
+
+MeanCO2 <- tapply(dataCO2$ObsCO2Comp, dataCO2$Year, mean)
+
+tmp <- ymd(paste0(unique(dataCO2$Year), "-06-15")) 
+MeanCO2Year <- data.frame(tmp , as.numeric(MeanCO2) )
+colnames(MeanCO2Year) <- c("Year", "MeanCO2") 
+dataCO2M <- merge( dataCO2, MeanCO2Year, by="Year")
+
+
+
+ggplot() +
+   geom_line(aes( x=dataCO2$Date, y=dataCO2$ObsCO2Comp), color='orange') +
+   geom_line(aes(x=MeanCO2Year$Year, y=MeanCO2Year$MeanCO2  ), color="blue") +
+  geom_line(aes(x=dataCO2$Date, y=tendance1  ), color="grey") +
+   #geom_line(aes(x=T, y=tendance1  ), color="grey") +
+    xlab("Year, Month") +
+    scale_x_date(date_labels = "%Y-%m", date_breaks = "5 year") +
+    theme(axis.text.x = element_text(face = "bold", color = "#993333", 
+                           size = 12, angle = 45, hjust = 1)) +
+    ylab("CO2 Concentration (ppm)") +
+    scale_y_continuous() +
+    theme(axis.text.y = element_text(face = "bold", color = "#993333", 
+                           size = 10, hjust = 1),axis.title.y = element_text(size = 10)) +
+  ggtitle("Graphique 1: Evolution au cours du temps de la teneur en CO2")
+

-
-

Modélisation

-

Série n’est pas stationnaire comme le montre le graphique

-

Série montre une saisonnalité

+
+

Modélisation de la série temporelle

+

On va chercher à modéliser la série en utilisant une catégorie de modèles qui cherche à déterminer chaque valeur de la série en fonction des valeurs qui la précède (yt = f(yt-1, yt-2, …)). C’est le cas des modèles ARIMA (“AutoRegressive – Integrated – Moving Average”). Cette catégorie de modèles a été popularisée et formalisée par Box et Jenkins (1976).

+

Les processus autorégressifs supposent que chaque point peut être prédit par la somme pondérée d’un ensemble de points précédents, plus un terme aléatoire d’erreur.

+

Le processus d’intégration suppose que chaque point présente une différence constante avec le point précédent.

+

Les processus de moyenne mobile supposent que chaque point est fonction des erreurs entachant les points précédant, plus sa propre erreur.

+

Un modèle ARIMA est étiqueté comme modèle ARIMA (p,d,q), dans lequel:

+
    +
  • p est le nombre de termes auto-régressifs
    • +
  • d est le nombre de différences
    • +
  • q est le nombre de moyennes mobiles.
    • +
+

On va utiliser la fonction auto.arima() qui est un algorithme automatique qui permet de trouver le modèle ARIMA qui estime le mieux la série temporelle.

+
Co2_train <- ts(dataCO2$ObsCO2Comp, start = c(1958,3), frequency = 12)
+Co2_train %>% ggtsdisplay()
+

+
auto.arima(Co2_train)
+
## Series: Co2_train 
+## ARIMA(1,1,1)(2,1,2)[12] 
+## 
+## Coefficients:
+##          ar1      ma1     sar1     sar2    sma1     sma2
+##       0.2188  -0.5797  -0.3038  -0.0090  -0.545  -0.2643
+## s.e.  0.0891   0.0746      NaN   0.0408     NaN      NaN
+## 
+## sigma^2 estimated as 0.09695:  log likelihood=-182.81
+## AIC=379.62   AICc=379.77   BIC=411.79
+

En se basant sur le résultat de l’analyse précédente, on retient le modèle \(ARIMA(1,1,1)(2,1,2)[12]\). On peut ensuite vérifier que les résidus ressemblent à un bruit blanc ou non.

+
(fit_minaicc <- Arima(Co2_train, order=c(1,1,1),seasonal=list(order=c(2,1,2),period=12),
+                  lambda = "auto"
+              ))
+
## Series: Co2_train 
+## ARIMA(1,1,1)(2,1,2)[12] 
+## Box Cox transformation: lambda= 0.3024523 
+## 
+## Coefficients:
+##          ar1      ma1     sar1     sar2     sma1     sma2
+##       0.2105  -0.5733  -0.3345  -0.0088  -0.5363  -0.3081
+## s.e.  0.0897   0.0757      NaN      NaN      NaN      NaN
+## 
+## sigma^2 estimated as 2.992e-05:  log likelihood=2824.66
+## AIC=-5635.33   AICc=-5635.17   BIC=-5603.16
+
checkresiduals(fit_minaicc, lag=36)
+

+
## 
+##  Ljung-Box test
+## 
+## data:  Residuals from ARIMA(1,1,1)(2,1,2)[12]
+## Q* = 25.374, df = 30, p-value = 0.7067
+## 
+## Model df: 6.   Total lags used: 36
+
fit_minaicc$aicc
+
## [1] -5635.174
+

Les graphiques précédents montre que le résidu ressemble suffisamment au bruit blanc, que la valeur p est élevée et que le modèle a passé le test de la Ljong-Box.

+
autoplot(forecast(fit_minaicc, h=200))
+

diff --git a/module3/exo3/exercice_en.Rmd b/module3/exo3/exercice_en.Rmd deleted file mode 100644 index 13b258d..0000000 --- a/module3/exo3/exercice_en.Rmd +++ /dev/null @@ -1,33 +0,0 @@ ---- -title: "Your title" -author: "Your name" -date: "Today's date" -output: html_document ---- - - -```{r setup, include=FALSE} -knitr::opts_chunk$set(echo = TRUE) -``` - -## Some explanations - -This is an R Markdown document that you can easily export to HTML, PDF, and MS Word formats. For more information on R Markdown, see . - -When you click on the button **Knit**, the document will be compiled in order to re-execute the R code and to include the results into the final document. As we have shown in the video, R code is inserted as follows: - -```{r cars} -summary(cars) -``` - -It is also straightforward to include figures. For example: - -```{r pressure, echo=FALSE} -plot(pressure) -``` - -Note the parameter `echo = FALSE` that indicates that the code will not appear in the final version of the document. We recommend not to use this parameter in the context of this MOOC, because we want your data analyses to be perfectly transparent and reproducible. - -Since the results are not stored in Rmd files, you should generate an HTML or PDF version of your exercises and commit them. Otherwise reading and checking your analysis will be difficult for anyone else but you. - -Now it's your turn! You can delete all this information and replace it by your computational document. diff --git a/module3/exo3/exercice_fr.Rmd b/module3/exo3/exercice_fr.Rmd deleted file mode 100644 index 7eece5e..0000000 --- a/module3/exo3/exercice_fr.Rmd +++ /dev/null @@ -1,33 +0,0 @@ ---- -title: "Votre titre" -author: "Votre nom" -date: "La date du jour" -output: html_document ---- - - -```{r setup, include=FALSE} -knitr::opts_chunk$set(echo = TRUE) -``` - -## Quelques explications - -Ceci est un document R markdown que vous pouvez aisément exporter au format HTML, PDF, et MS Word. Pour plus de détails sur R Markdown consultez . - -Lorsque vous cliquerez sur le bouton **Knit** ce document sera compilé afin de ré-exécuter le code R et d'inclure les résultats dans un document final. Comme nous vous l'avons montré dans la vidéo, on inclue du code R de la façon suivante: - -```{r cars} -summary(cars) -``` - -Et on peut aussi aisément inclure des figures. Par exemple: - -```{r pressure, echo=FALSE} -plot(pressure) -``` - -Vous remarquerez le paramètre `echo = FALSE` qui indique que le code ne doit pas apparaître dans la version finale du document. Nous vous recommandons dans le cadre de ce MOOC de ne pas utiliser ce paramètre car l'objectif est que vos analyses de données soient parfaitement transparentes pour être reproductibles. - -Comme les résultats ne sont pas stockés dans les fichiers Rmd, pour faciliter la relecture de vos analyses par d'autres personnes, vous aurez donc intérêt à générer un HTML ou un PDF et à le commiter. - -Maintenant, à vous de jouer! Vous pouvez effacer toutes ces informations et les remplacer par votre document computationnel. diff --git a/module3/exo3/weekly_in_situ_co2_mlo.csv b/module3/exo3/weekly_in_situ_co2_mlo.csv new file mode 100644 index 0000000..78ae227 --- /dev/null +++ b/module3/exo3/weekly_in_situ_co2_mlo.csv @@ -0,0 +1,3210 @@ +"-------------------------------------------------------------------------------------------" +" Atmospheric CO2 concentrations (ppm) derived from in situ air measurements " +" at Mauna Loa, Observatory, Hawaii: Latitude 19.5°N Longitude 155.6°W Elevation 3397m " +" " +" Source: R. F. Keeling, S. J. Walker, S. C. Piper and A. F. Bollenbacher " +" Scripps CO2 Program ( http://scrippsco2.ucsd.edu ) " +" Scripps Institution of Oceanography (SIO) " +" University of California " +" La Jolla, California USA 92093-0244 " +" " +" Status of data and correspondence: " +" " +" These data are subject to revision based on recalibration of standard gases. Questions " +" about the data should be directed to Dr. Ralph Keeling (rkeeling@ucsd.edu), Stephen Walker" +" (sjwalker@ucsd.edu) and Stephen Piper (scpiper@ucsd.edu), Scripps CO2 Program. " +" " +" Baseline data in this file through 17-Apr-2020 from archive dated 20-Apr-2020 08:06:03 " +" " +"-------------------------------------------------------------------------------------------" +" " +" Please cite as: " +" " +" C. D. Keeling, S. C. Piper, R. B. Bacastow, M. Wahlen, T. P. Whorf, M. Heimann, and " +" H. A. Meijer, Exchanges of atmospheric CO2 and 13CO2 with the terrestrial biosphere and " +" oceans from 1978 to 2000. I. Global aspects, SIO Reference Series, No. 01-06, Scripps " +" Institution of Oceanography, San Diego, 88 pages, 2001. " +" " +" If it is necessary to cite a peer-reviewed article, please cite as: " +" " +" C. D. Keeling, S. C. Piper, R. B. Bacastow, M. Wahlen, T. P. Whorf, M. Heimann, and " +" H. A. Meijer, Atmospheric CO2 and 13CO2 exchange with the terrestrial biosphere and " +" oceans from 1978 to 2000: observations and carbon cycle implications, pages 83-113, " +" in "A History of Atmospheric CO2 and its effects on Plants, Animals, and Ecosystems", " +" editors, Ehleringer, J.R., T. E. Cerling, M. D. Dearing, Springer Verlag, " +" New York, 2005. " +" " +"-------------------------------------------------------------------------------------------" +" " +" " +" The data file below contains 2 columns indicaing the date and CO2 " +" concentrations in micro-mol CO2 per mole (ppm), reported on the 2008A " +" SIO manometric mole fraction scale. These weekly values have been " +" adjusted to 12:00 hours at middle day of each weekly period as " +" indicated by the date in the first column. " +1958-03-29, 316.19 +1958-04-05, 317.31 +1958-04-12, 317.69 +1958-04-19, 317.58 +1958-04-26, 316.48 +1958-05-03, 316.95 +1958-05-17, 317.56 +1958-05-24, 317.99 +1958-07-05, 315.85 +1958-07-12, 315.85 +1958-07-19, 315.46 +1958-07-26, 315.59 +1958-08-02, 315.64 +1958-08-09, 315.10 +1958-08-16, 315.09 +1958-08-30, 314.14 +1958-09-06, 313.54 +1958-11-08, 313.05 +1958-11-15, 313.26 +1958-11-22, 313.57 +1958-11-29, 314.01 +1958-12-06, 314.56 +1958-12-13, 314.41 +1958-12-20, 314.77 +1958-12-27, 315.21 +1959-01-03, 315.24 +1959-01-10, 315.50 +1959-01-17, 315.69 +1959-01-24, 315.86 +1959-01-31, 315.42 +1959-02-14, 316.94 +1959-02-21, 316.61 +1959-02-28, 316.62 +1959-03-07, 316.81 +1959-03-21, 316.73 +1959-03-28, 316.71 +1959-04-04, 317.72 +1959-04-11, 317.12 +1959-04-18, 317.64 +1959-04-25, 318.32 +1959-05-02, 318.27 +1959-05-09, 318.78 +1959-05-16, 318.05 +1959-05-23, 318.43 +1959-06-06, 318.53 +1959-06-13, 318.14 +1959-06-20, 317.88 +1959-06-27, 317.76 +1959-07-04, 316.86 +1959-07-11, 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401.03 +2015-03-07, 401.63 +2015-03-14, 401.80 +2015-03-21, 400.79 +2015-03-28, 402.50 +2015-04-04, 402.74 +2015-04-11, 403.88 +2015-04-18, 403.80 +2015-04-25, 403.22 +2015-05-02, 404.07 +2015-05-09, 404.09 +2015-05-16, 404.31 +2015-05-23, 403.85 +2015-05-30, 403.81 +2015-06-06, 403.45 +2015-06-13, 402.72 +2015-06-20, 402.63 +2015-06-27, 402.36 +2015-07-04, 402.25 +2015-07-11, 401.71 +2015-07-18, 401.02 +2015-07-25, 401.30 +2015-08-01, 398.74 +2015-08-08, 399.21 +2015-08-15, 399.12 +2015-08-22, 399.03 +2015-08-29, 398.80 +2015-09-05, 398.16 +2015-09-12, 397.10 +2015-09-19, 397.57 +2015-09-26, 397.42 +2015-10-03, 397.74 +2015-10-10, 398.51 +2015-10-17, 398.61 +2015-10-24, 398.43 +2015-10-31, 398.87 +2015-11-07, 399.53 +2015-11-14, 400.75 +2015-11-21, 400.42 +2015-11-28, 400.83 +2015-12-05, 400.91 +2015-12-12, 402.40 +2015-12-19, 402.32 +2015-12-26, 402.01 +2016-01-02, 402.25 +2016-01-09, 402.23 +2016-01-16, 402.68 +2016-01-23, 403.26 +2016-01-30, 402.79 +2016-02-06, 404.98 +2016-02-13, 403.22 +2016-02-20, 404.59 +2016-02-27, 403.98 +2016-03-05, 403.99 +2016-03-12, 404.51 +2016-03-19, 405.01 +2016-03-26, 406.16 +2016-04-02, 405.70 +2016-04-09, 408.56 +2016-04-16, 408.16 +2016-04-23, 407.70 +2016-04-30, 407.84 +2016-05-07, 407.51 +2016-05-14, 407.54 +2016-05-21, 407.41 +2016-05-28, 407.92 +2016-06-04, 407.52 +2016-06-11, 406.99 +2016-06-18, 407.02 +2016-06-25, 406.40 +2016-07-02, 405.96 +2016-07-09, 404.93 +2016-07-16, 403.64 +2016-07-23, 403.71 +2016-07-30, 403.76 +2016-08-06, 403.22 +2016-08-13, 402.11 +2016-08-20, 401.78 +2016-08-27, 401.43 +2016-09-03, 401.27 +2016-09-10, 401.13 +2016-09-17, 401.25 +2016-09-24, 400.85 +2016-10-01, 400.82 +2016-10-08, 401.20 +2016-10-15, 401.70 +2016-10-22, 401.82 +2016-10-29, 402.38 +2016-11-05, 403.15 +2016-11-12, 403.12 +2016-11-19, 403.95 +2016-11-26, 404.44 +2016-12-03, 404.16 +2016-12-10, 404.28 +2016-12-17, 404.63 +2016-12-24, 404.66 +2016-12-31, 405.38 +2017-01-07, 405.94 +2017-01-14, 405.91 +2017-01-21, 406.37 +2017-01-28, 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409.26 +2019-01-05, 410.32 +2019-01-12, 409.73 +2019-01-19, 412.31 +2019-01-26, 410.91 +2019-02-02, 410.97 +2019-02-09, 412.12 +2019-02-16, 411.79 +2019-02-23, 411.46 +2019-03-02, 412.08 +2019-03-09, 412.26 +2019-03-16, 412.87 +2019-03-23, 410.73 +2019-03-30, 412.37 +2019-04-06, 412.62 +2019-04-13, 413.36 +2019-04-20, 413.94 +2019-04-27, 414.27 +2019-05-04, 414.41 +2019-05-11, 414.95 +2019-05-18, 415.08 +2019-05-25, 414.66 +2019-06-01, 414.21 +2019-06-08, 414.45 +2019-06-15, 413.85 +2019-06-22, 413.68 +2019-06-29, 413.38 +2019-07-06, 412.69 +2019-07-13, 412.30 +2019-07-20, 411.76 +2019-07-27, 410.32 +2019-08-03, 410.50 +2019-08-10, 410.48 +2019-08-17, 410.05 +2019-08-24, 409.52 +2019-08-31, 409.32 +2019-09-07, 408.80 +2019-09-14, 408.61 +2019-09-21, 408.50 +2019-09-28, 408.28 +2019-10-05, 407.99 +2019-10-12, 408.61 +2019-10-19, 408.77 +2019-10-26, 408.68 +2019-11-02, 409.86 +2019-11-09, 410.15 +2019-11-16, 410.22 +2019-11-23, 410.48 +2019-11-30, 410.92 +2019-12-07, 411.27 +2019-12-14, 411.67 +2019-12-21, 412.30 +2019-12-28, 412.59 +2020-01-04, 413.19 +2020-01-11, 413.39 +2020-01-25, 413.36 +2020-02-01, 413.99 +2020-02-08, 414.83 +2020-02-15, 413.81 +2020-02-22, 414.17 +2020-02-29, 413.89 +2020-03-07, 414.00 +2020-03-14, 414.30 +2020-03-21, 414.62 +2020-03-28, 415.57 +2020-04-04, 415.61 +2020-04-11, 416.47 -- 2.18.1