# Assignment $12$

library$($fpp$3)$

# $12\mathrm{.}2$ Fit VAR model with AICc and BIC for Consumption, Income, and Savings

fit $<-$ us$\_$change $\%>\%$

model$($

aicc $=$ VAR$($vars$($Consumption$,$ Income, Savings$)),$

bic $=$ VAR$($vars$($Consumption$,$ Income, Savings$),$ ic $=$ "bic"$)$

$)$

fit

glance$($fit$)$

# $12\mathrm{.}3$ ACF of the residuals

fit $\%>\%$

augment$()\%>\%$

ACF$(.$innov$)\%>\%$

autoplot$()$

# VAR$(5)$ forecasts using the model suggested by AICc

forecast$\_$plots $<-$ fit $\%>\%$

select$($aicc$)\%>\%$

forecast$($h $="2$ years"$)\%>\%$

filter$($year$($Quarter$)>2000)\%>\%$

autoplot$($us$\_$change $\%>\%$ filter$($year$($Quarter$)>2000))$

forecast$\_$plots

if $(!$requireNamespace$("$broom$",$ quietly $=$ TRUE$))\{$

install.packages$("$broom$")$

$\}$

$4.$Use the model suggested by the AICc criterion to forecast the three variables. Choose $$year$($Quarter$)>2000.$

Paste here: the forecast plots for the three variables.

$5.$Run $$report$($fit$)$ for the AICc suggested model. The output will show an estimated equation for each of the variables in the VAR model. Given the estimated coefficients, write out the VAR model similar to equations $12\mathrm{.}1$ and $12\mathrm{.}2.$ Do not include the error terms.

Paste here: the report$($fit$)$ output.

$6.$Compute the forecast values for consumption, income, and savings.

Paste here: The fable with the forecast values