$11.$ Consider the following bivariate VAR model: y$1$t $=0\mathrm{.}3$y$1,$t$1+0\mathrm{.}8$y$2,$t$1+$ a$1$t $,$ y$2$t $=0\mathrm{.}9$y$1,$t$1+0\mathrm{.}4$y$2,$t$1+$ a$2$t $,$ with E$($a$1$ta$1$ $)=1$ if t $=$ and $0$ otherwise, E$($a$2$ta$2$ $)=2$ if t $=$ and $0$ otherwise, and E$($a$1$ta$2$ $)=0$ for all t and $.($a$).$ Is this system stationary? $($b$).$ Calculate the two$-$step ahead forecast variance for variable y$1,$t$+2,$ that is E$[$y$1,$t$+2$ E$($y$1,$t$+2|$Yt $,$ Yt$1,)]2,$ where Yt $=($y$1$t $,$ y$2$t$).$