code class$=$"asciimath"$>(30$ points$)$ Suppose that the monthly log return of a security r$\_($t$)$ follows the model r$\_($t$)=0\mathrm{.}02+0\mathrm{.}1$r$\_($t$-1)+$a$\_($t$)+0\mathrm{.}2$a$\_($t$-1)$ where $\{$a$\_($t$)\}$ is a Gaussian white noise series with mean zero and variance $0\mathrm{.}01.($a$)$ Compute the mean and variance of the return series. $(6$ points$)($b$)$ Compute the autocorrelations of the return series for all lags. $(14$ points$)($c$)$ Compute the $1-$step$-$ and all the multistep$-$ahead forecasts of the return at the forecast origin t$=$h$.(10$ points$)$