comportement_marco
Aristidina
2025-05-27
Importation et chargement de la base
library(readxl)
library(ggplot2)
library(tidyr)
base_bot <- read_excel("C:/Users/DELL/Desktop/base_bot.xlsx", sheet = "Base")
head(base_bot)## # A tibble: 6 × 4
## Annee C PIB_r RNB
## <chr> <dbl> <dbl> <dbl>
## 1 1990 3139079431. 5274313873. 5163084155.
## 2 1991 3364466918. 5667709608. 5712056669.
## 3 1992 3480302391. 5833040675. 5920640884.
## 4 1993 3575602576. 5944807979. 6208045254.
## 5 1994 3702263332. 6160480628. 5932196869.
## 6 1995 4142509121. 6593587690. 6546735502.base_bot$Annee <- as.numeric(base_bot$Annee)
attach(base_bot)2. Statistiques descriptives
summary(base_bot)## Annee C PIB_r RNB
## Min. :1990 Min. :3.139e+09 Min. :5.274e+09 Min. :5.163e+09
## 1st Qu.:1998 1st Qu.:4.844e+09 1st Qu.:7.592e+09 1st Qu.:7.697e+09
## Median :2006 Median :6.168e+09 Median :1.031e+10 Median :1.021e+10
## Mean :2006 Mean :7.261e+09 Mean :1.071e+10 Mean :1.037e+10
## 3rd Qu.:2014 3rd Qu.:1.031e+10 3rd Qu.:1.353e+10 3rd Qu.:1.308e+10
## Max. :2022 Max. :1.299e+10 Max. :1.747e+10 Max. :1.745e+10sd(PIB_r)## [1] 3599830167sd(C)## [1] 3159746217sd(RNB)## [1] 3475180701data_long <- pivot_longer(base_bot, cols = c(PIB_r, C, RNB),
names_to = "Variable",
values_to = "Valeur")
# Tracer toutes les courbes sur un même graphique
ggplot(data_long, aes(x = Annee, y = Valeur, color = Variable)) +
geom_line(size = 1.3) +
labs(
title = "Évolution du PIB, de la Consommation et du RNB au Botswana (1990–2022)",
x = "Année",
y = "Valeur (en USD constants)",
color = "Variables macroéconomiques"
) +
scale_color_manual(
values = c(
"PIB_r" = "#e75480", # rose vif
"C" = "#d896d8", # rose mauve
"RNB" = "#c71585" # violet rosé foncé
),
labels = c("PIB", "Consommation", "RNB")
) +
theme_minimal() +
theme(
plot.title = element_text(face = "bold", size = 14),
axis.title = element_text(size = 12),
legend.title = element_text(size = 11),
legend.text = element_text(size = 10)
)## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
3. Corrélations
library(corrplot)## Warning: package 'corrplot' was built under R version 4.4.1## corrplot 0.94 loadedvars <- base_bot[, c("PIB_r", "C", "RNB")]
# Calcul de la matrice de corrélation
cor_matrix <- cor(vars, use = "complete.obs")
# Visualisation élégante
corrplot(cor_matrix, method = "color",
type = "upper", # Affiche la moitié supérieure
col = colorRampPalette(c("#fbe1e7", "#fa8ea4", "#fa8eb2"))(200), # Palette rose-violet
tl.col = "black", # Couleur des labels
tl.cex = 1.2, # Taille du texte
addCoef.col = "black", # Affiche les coefficients
number.cex = 1.1, # Taille des coefficients
title = "Matrice de corrélation entre PIB_r, C et RNB",
mar = c(0,0,2,0)) # Marge pour le ti
# 4. Régression pour la PMC (avec PIB)
model_pmc_pib <- lm(C ~ PIB_r)
summary(model_pmc_pib)##
## Call:
## lm(formula = C ~ PIB_r)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.346e+09 -3.530e+08 2.335e+08 4.026e+08 1.494e+09
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.903e+09 3.956e+08 -4.809 3.71e-05 ***
## PIB_r 8.558e-01 3.507e-02 24.398 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 714200000 on 31 degrees of freedom
## Multiple R-squared: 0.9505, Adjusted R-squared: 0.9489
## F-statistic: 595.3 on 1 and 31 DF, p-value: < 2.2e-165. Régression pour la PMC (avec RNB)
model_pmc_rnb <- lm(C ~ RNB)
summary(model_pmc_rnb)##
## Call:
## lm(formula = C ~ RNB)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.388e+09 -5.715e+08 1.294e+08 4.080e+08 1.067e+09
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.985e+09 3.527e+08 -5.629 3.53e-06 ***
## RNB 8.913e-01 3.228e-02 27.609 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 634600000 on 31 degrees of freedom
## Multiple R-squared: 0.9609, Adjusted R-squared: 0.9597
## F-statistic: 762.3 on 1 and 31 DF, p-value: < 2.2e-16C =f(Y)
plot(C ~ PIB_r, main="Consommation en fonction du PIB", xlab="PIB", ylab="Consommation")
abline(lm(C ~ PIB_r, data=base_bot), col="#c71585")
plot(C ~ RNB, main="Consommation en fonction du RNB", xlab="RNB", ylab="Consommation")
abline(lm(C ~ RNB, data=base_bot), col="#c71585")
# AR ## Transformer en série temporelle
library(tseries)## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoolibrary(urca)
library(forecast)
Y <- ts(PIB_r, start = 1990, frequency = 1)# 2. Test de stationnarité
adf_result <- adf.test(Y)
print(adf_result)##
## Augmented Dickey-Fuller Test
##
## data: Y
## Dickey-Fuller = -3.0277, Lag order = 3, p-value = 0.1756
## alternative hypothesis: stationaryY_diff <- diff(Y)
adf_resultdif <- adf.test(Y_diff)## Warning in adf.test(Y_diff): p-value smaller than printed p-valueprint(adf_resultdif)##
## Augmented Dickey-Fuller Test
##
## data: Y_diff
## Dickey-Fuller = -4.7363, Lag order = 3, p-value = 0.01
## alternative hypothesis: stationary##correlogramme
par(mfrow = c(1,2)) # 2 graphiques côte à côte
acf(Y, main = "ACF du PIB ", col = "#c71585")
pacf(Y, main = "PACF du PIB ", col = "purple")
par(mfrow = c(1,1)) # Réinitialiserpar(mfrow = c(1,2)) # 2 graphiques côte à côte
acf(Y_diff, main = "ACF du PIB différencié", col = "#c71585")
pacf(Y_diff, main = "PACF du PIB différencié", col = "purple")
par(mfrow = c(1,1)) # RéinitialiserAjuster un modèle AR(2)
model_ar2 <- arima(Y, order = c(2, 1, 0))
summary(model_ar2)##
## Call:
## arima(x = Y, order = c(2, 1, 0))
##
## Coefficients:
## ar1 ar2
## 0.0135 0.0090
## s.e. 0.1792 0.1932
##
## sigma^2 estimated as 5.866e+17: log likelihood = -700.02, aic = 1406.03
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 362466878 754182779 598214339 3.357767 5.286656 0.9646854
## ACF1
## Training set -0.2901335model_ar1 <- arima(Y, order = c(1, 1, 0))
model_ar1##
## Call:
## arima(x = Y, order = c(1, 1, 0))
##
## Coefficients:
## ar1
## 0.0128
## s.e. 0.1786
##
## sigma^2 estimated as 5.866e+17: log likelihood = -700.02, aic = 1404.03best_model <- auto.arima(Y)
summary(best_model)## Series: Y
## ARIMA(0,1,0) with drift
##
## Coefficients:
## drift
## 381093145
## s.e. 102454471
##
## sigma^2 = 4.557e+17: log likelihood = -695.47
## AIC=1394.94 AICc=1395.35 BIC=1397.87
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 148279.3 654291453 427449402 -0.3667388 3.70096 0.6893084
## ACF1
## Training set -0.2874421Comparaison avec AR(1)
AIC(model_ar1); AIC(model_ar2)## [1] 1404.033## [1] 1406.03Test de significativité des coefficients
coeftest <- function(model) {
coef <- model$coef
se <- sqrt(diag(model$var.coef))
tval <- coef / se
pval <- 2 * (1 - pnorm(abs(tval)))
data.frame(Coefficient = coef, `Std. Error` = se, `t value` = tval, `Pr(>|t|)` = pval)
}
coeftest(model_ar2)## Coefficient Std..Error t.value Pr...t..
## ar1 0.013520358 0.1792000 0.07544843 0.9398579
## ar2 0.009046208 0.1931616 0.04683233 0.9626469coeftest(model_ar1)## Coefficient Std..Error t.value Pr...t..
## ar1 0.01282455 0.1786411 0.07178946 0.9427695coeftest(best_model)## Coefficient Std..Error t.value Pr...t..
## drift 381093145 102454471 3.719634 0.0001995116