Laboratorio 7
Luis Pedro Aguilar Paz
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':
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## as.Date, as.Date.numeric## Loading required package: sandwich## Loading required package: urca## Loading required package: lmtestlibrary(fpp2)## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo## ── Attaching packages ────────────────────────────────────────────── fpp2 2.5 ──## ✔ ggplot2 3.4.0 ✔ fma 2.5
## ✔ forecast 8.20 ✔ 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':
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## acf, arima## The following object is masked from 'package:utils':
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## tarseries<-uschange
autoplot(uschange[,c(2,5)])
ts.plot(series[,c(2,5)], xlab="Tiempo",col=c(1,3))
Utilizamos las variables ingreso y desempleo.
Búsqueda de parámetros y creación del modelo
a <- VARselect(uschange[,c(2,5)], lag.max=15,type="const")
a$selection## AIC(n) HQ(n) SC(n) FPE(n)
## 8 1 1 8El modelo sugiere utilizar 8 lags, sin embargo al utilizar 8 el modelo presenta autocorrelación e incluye variables que no son significativas al modelo.
modelo1<-VAR(uschange[,c(2,5)],p=5,type=c("const"))
modelo_s<-summary(modelo1)modelo_s$roots## [1] 0.7775660 0.7775660 0.7660914 0.7660914 0.7488061 0.7488061 0.6720236
## [8] 0.6720236 0.6364359 0.5646411summary(modelo1,equation="Income")##
## VAR Estimation Results:
## =========================
## Endogenous variables: Income, Unemployment
## Deterministic variables: const
## Sample size: 182
## Log Likelihood: -262.292
## Roots of the characteristic polynomial:
## 0.7776 0.7776 0.7661 0.7661 0.7488 0.7488 0.672 0.672 0.6364 0.5646
## Call:
## VAR(y = uschange[, c(2, 5)], p = 5, type = c("const"))
##
##
## Estimation results for equation Income:
## =======================================
## Income = Income.l1 + Unemployment.l1 + Income.l2 + Unemployment.l2 + Income.l3 + Unemployment.l3 + Income.l4 + Unemployment.l4 + Income.l5 + Unemployment.l5 + const
##
## Estimate Std. Error t value Pr(>|t|)
## Income.l1 -0.13069 0.07628 -1.713 0.08848 .
## Unemployment.l1 -0.47812 0.22736 -2.103 0.03693 *
## Income.l2 0.08289 0.07790 1.064 0.28883
## Unemployment.l2 0.39251 0.23868 1.644 0.10191
## Income.l3 0.03524 0.07602 0.464 0.64351
## Unemployment.l3 -0.65814 0.24414 -2.696 0.00773 **
## Income.l4 -0.09359 0.07556 -1.239 0.21717
## Unemployment.l4 -0.14117 0.24531 -0.575 0.56571
## Income.l5 -0.12761 0.07471 -1.708 0.08944 .
## Unemployment.l5 0.39764 0.22214 1.790 0.07522 .
## const 0.87038 0.14889 5.846 2.49e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.8936 on 171 degrees of freedom
## Multiple R-Squared: 0.1347, Adjusted R-squared: 0.08413
## F-statistic: 2.663 on 10 and 171 DF, p-value: 0.004781
##
##
##
## Covariance matrix of residuals:
## Income Unemployment
## Income 0.7985 -0.05280
## Unemployment -0.0528 0.09033
##
## Correlation matrix of residuals:
## Income Unemployment
## Income 1.0000 -0.1966
## Unemployment -0.1966 1.0000summary(modelo1,equation="Unemployment")##
## VAR Estimation Results:
## =========================
## Endogenous variables: Income, Unemployment
## Deterministic variables: const
## Sample size: 182
## Log Likelihood: -262.292
## Roots of the characteristic polynomial:
## 0.7776 0.7776 0.7661 0.7661 0.7488 0.7488 0.672 0.672 0.6364 0.5646
## Call:
## VAR(y = uschange[, c(2, 5)], p = 5, type = c("const"))
##
##
## Estimation results for equation Unemployment:
## =============================================
## Unemployment = Income.l1 + Unemployment.l1 + Income.l2 + Unemployment.l2 + Income.l3 + Unemployment.l3 + Income.l4 + Unemployment.l4 + Income.l5 + Unemployment.l5 + const
##
## Estimate Std. Error t value Pr(>|t|)
## Income.l1 -0.050174 0.025657 -1.956 0.05215 .
## Unemployment.l1 0.436087 0.076472 5.703 5.08e-08 ***
## Income.l2 -0.004766 0.026202 -0.182 0.85589
## Unemployment.l2 0.156143 0.080280 1.945 0.05342 .
## Income.l3 -0.023081 0.025569 -0.903 0.36796
## Unemployment.l3 0.067925 0.082118 0.827 0.40930
## Income.l4 -0.012685 0.025414 -0.499 0.61833
## Unemployment.l4 -0.183030 0.082510 -2.218 0.02785 *
## Income.l5 0.068785 0.025128 2.737 0.00685 **
## Unemployment.l5 0.038701 0.074718 0.518 0.60516
## const 0.012796 0.050080 0.256 0.79863
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.3006 on 171 degrees of freedom
## Multiple R-Squared: 0.3665, Adjusted R-squared: 0.3295
## F-statistic: 9.893 on 10 and 171 DF, p-value: 5.479e-13
##
##
##
## Covariance matrix of residuals:
## Income Unemployment
## Income 0.7985 -0.05280
## Unemployment -0.0528 0.09033
##
## Correlation matrix of residuals:
## Income Unemployment
## Income 1.0000 -0.1966
## Unemployment -0.1966 1.0000Hay ciertos lags de las variables que no son significativos al modelo, por lo que se podria considerar eliminarlos del modelo.
Pruebas del Modelo
serial.test(modelo1, lags.pt=10, type="PT.asymptotic")##
## Portmanteau Test (asymptotic)
##
## data: Residuals of VAR object modelo1
## Chi-squared = 31.773, df = 20, p-value = 0.04577El modelo no presenta autocorrelación.
roots(modelo1)## [1] 0.7775660 0.7775660 0.7660914 0.7660914 0.7488061 0.7488061 0.6720236
## [8] 0.6720236 0.6364359 0.5646411El modelo no tiene raices unitarias por lo que es estacionaria.
normality.test(modelo1, multivariate.only=FALSE)## $Income
##
## JB-Test (univariate)
##
## data: Residual of Income equation
## Chi-squared = 195.51, df = 2, p-value < 2.2e-16
##
##
## $Unemployment
##
## JB-Test (univariate)
##
## data: Residual of Unemployment equation
## Chi-squared = 33.197, df = 2, p-value = 6.184e-08
##
##
## $JB
##
## JB-Test (multivariate)
##
## data: Residuals of VAR object modelo1
## Chi-squared = 216.79, df = 4, p-value < 2.2e-16
##
##
## $Skewness
##
## Skewness only (multivariate)
##
## data: Residuals of VAR object modelo1
## Chi-squared = 7.8916, df = 2, p-value = 0.01934
##
##
## $Kurtosis
##
## Kurtosis only (multivariate)
##
## data: Residuals of VAR object modelo1
## Chi-squared = 208.9, df = 2, p-value < 2.2e-16En la prueba de normalidad el p.value es < 0.05 por lo que nuestro modelo es normal.
arch<-arch.test(modelo1, lags.multi = 12, multivariate.only = FALSE)
arch## $Income
##
## ARCH test (univariate)
##
## data: Residual of Income equation
## Chi-squared = 11.621, df = 16, p-value = 0.7697
##
##
## $Unemployment
##
## ARCH test (univariate)
##
## data: Residual of Unemployment equation
## Chi-squared = 21.391, df = 16, p-value = 0.164
##
##
##
## ARCH (multivariate)
##
## data: Residuals of VAR object modelo1
## Chi-squared = 121.69, df = 108, p-value = 0.1737El modelo no presenta heteroscedasticidad ya que el p.value es > 0.05
arch<-arch.test(modelo1, lags.multi = 12, multivariate.only = FALSE)
arch## $Income
##
## ARCH test (univariate)
##
## data: Residual of Income equation
## Chi-squared = 11.621, df = 16, p-value = 0.7697
##
##
## $Unemployment
##
## ARCH test (univariate)
##
## data: Residual of Unemployment equation
## Chi-squared = 21.391, df = 16, p-value = 0.164
##
##
##
## ARCH (multivariate)
##
## data: Residuals of VAR object modelo1
## Chi-squared = 121.69, df = 108, p-value = 0.1737El modelo no presenta quiebres estructurales, ambas gráficas no salen de los parámetros tolerados.
Respuesta de impulso
UnemploymentIRF <- irf(modelo1, impulse = "Income", response="Unemployment", n.ahead = 20, boot = T )
plot(UnemploymentIRF, ylab = "Unemploymet", main = "Shock desde Income")
IncomeIRF <- irf(modelo1, impulse = "Unemployment", response="Income", n.ahead = 20, boot = T )
plot(IncomeIRF, ylab = "Income", main = "Shock desde Unemployment")
Ambas variables en sus gráficas se estabilizan y vuelven a la normalidad después del shock.
Descomposición de la varianza
FEVD1 <- fevd(modelo1, n.ahead = 10)
plot(FEVD1)
En el ingreso se observa que aunque en menor medida tiene relación con el desempleo. De igual forma para el desempleo.
Predicción
fore<-predict(modelo1, n.ahead = 10, ci=0.95)
fanchart(fore)
Fórmula
modelo1$varresult$Income$coefficients## Income.l1 Unemployment.l1 Income.l2 Unemployment.l2 Income.l3
## -0.13068647 -0.47812026 0.08288524 0.39250556 0.03524393
## Unemployment.l3 Income.l4 Unemployment.l4 Income.l5 Unemployment.l5
## -0.65813631 -0.09359142 -0.14117449 -0.12760511 0.39764021
## const
## 0.87038486modelo1$varresult$Unemployment$coefficients## Income.l1 Unemployment.l1 Income.l2 Unemployment.l2 Income.l3
## -0.050173536 0.436086896 -0.004765779 0.156142861 -0.023081051
## Unemployment.l3 Income.l4 Unemployment.l4 Income.l5 Unemployment.l5
## 0.067925032 -0.012685006 -0.183030356 0.068785222 0.038700766
## const
## 0.012796215autoplot(forecast(modelo1))