LAB#6

LABORATORIO 6

library(vars)

## Loading required package: MASS

## Loading required package: strucchange

## Loading required package: zoo

## 
## Attaching package: 'zoo'

## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric

## Loading required package: sandwich

## Loading required package: urca

## Loading required package: lmtest

library(fpp2)

## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo

## ── Attaching packages ────────────────────────────────────────────── fpp2 2.5 ──

## ✔ ggplot2   3.4.1     ✔ fma       2.5  
## ✔ forecast  8.21      ✔ expsmooth 2.3

## 

library(TSA)

## Registered S3 methods overwritten by 'TSA':
##   method       from    
##   fitted.Arima forecast
##   plot.Arima   forecast

## 
## Attaching package: 'TSA'

## The following objects are masked from 'package:stats':
## 
##     acf, arima

## The following object is masked from 'package:utils':
## 
##     tar

series <- autoplot(uschange)
autoplot(uschange[,c(2:4)])

a <- VARselect(uschange[,c(2,4)], lag.max=15,type="trend")
a$selection

## AIC(n)  HQ(n)  SC(n) FPE(n) 
##      3      3      1      3

Los valores que se recomiendan para P son 1 y 3.

Se evaluaran 2 modelos

modelo1<-VAR(uschange[,c(2:4)],p=1,type=c("trend"))
modelo3<-VAR(uschange[,c(2:4)],p=3,type=c("trend"))

aic1<-summary(modelo1)$logLik
aic2<-summary(modelo3)$logLik

serial.test(modelo1, lags.pt=10, type="PT.asymptotic")

## 
##  Portmanteau Test (asymptotic)
## 
## data:  Residuals of VAR object modelo1
## Chi-squared = 137.67, df = 81, p-value = 8.763e-05

serial.test(modelo3, lags.pt=10, type="PT.asymptotic")

## 
##  Portmanteau Test (asymptotic)
## 
## data:  Residuals of VAR object modelo3
## Chi-squared = 75.303, df = 63, p-value = 0.1378

roots(modelo1)

## [1] 0.4816638 0.4816638 0.3158780

roots(modelo3)

## [1] 0.8688517 0.5809402 0.5809402 0.5679856 0.5679856 0.5427566 0.4075580
## [8] 0.4075580 0.1279951

Todas los valores de las raíces unitarias estan por encima de 0.05

stab<-stability(modelo1, type = "OLS-CUSUM")
plot(stab)

La mejor opción es el modelo 1 que contiene una P = 1