For this week i will use colombia’s GDP and Procolombia’s Exports between 2009 and 2022.
PIB_Export <- read_excel("~/Desktop/PIB_Export.xlsx")
t=seq(2009.1,2022.2, length.out=length(PIB_Export$DATE))
export<-ts(PIB_Export$EXPORT1,frequency=4,start=c(2005,1))
plot(export)
Following Colombia’s department of statistics, this series controls for stationary effects. We can see clearly the positive trend.
GDP<-ts(PIB_Export$GDP,frequency=4,start=c(2005,1))
plot(GDP)
acf(GDP)
plot(diff(GDP))
acf(diff(GDP))
Here we don’t have any significant lag. First difference works in this case.
PIB_Export <- na.omit(PIB_Export)
vardata = subset(PIB_Export, select = c(GDP,EXPORT1) )
VARselect(vardata, lag.max = 8, type = "const")$selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 4 4 4 4
VAR1 <- VAR(vardata, p = 4, type = "const")
VAR1
##
## VAR Estimation Results:
## =======================
##
## Estimated coefficients for equation GDP:
## ========================================
## Call:
## GDP = GDP.l1 + EXPORT1.l1 + GDP.l2 + EXPORT1.l2 + GDP.l3 + EXPORT1.l3 + GDP.l4 + EXPORT1.l4 + const
##
## GDP.l1 EXPORT1.l1 GDP.l2 EXPORT1.l2 GDP.l3
## 9.184849e-01 -3.501472e-06 6.522598e-02 7.148131e-06 -1.388338e-01
## EXPORT1.l3 GDP.l4 EXPORT1.l4 const
## 8.397840e-06 6.788083e-02 5.709185e-07 1.336762e+04
##
##
## Estimated coefficients for equation EXPORT1:
## ============================================
## Call:
## EXPORT1 = GDP.l1 + EXPORT1.l1 + GDP.l2 + EXPORT1.l2 + GDP.l3 + EXPORT1.l3 + GDP.l4 + EXPORT1.l4 + const
##
## GDP.l1 EXPORT1.l1 GDP.l2 EXPORT1.l2 GDP.l3
## 4.562427e+03 5.368368e-03 -3.731246e+03 -2.048899e-01 1.246175e+04
## EXPORT1.l3 GDP.l4 EXPORT1.l4 const
## 9.741074e-02 -9.743765e+03 8.301648e-01 -4.652709e+08
tsdisplay(residuals(VAR1))
In both graphs we see a significant lag in 4.
predict1 <- predict(VAR1, n.ahead = 4)
plot(predict1)