Q$(1)$a$)$ Using daily return series for the stock of XYZ$,$ the parameters estimates for a GARCH$(1,1)$ model for the conditional variance are $\backslash$omega $=0\mathrm{.}000005,\backslash$alpha $=0\mathrm{.}05$ and $\backslash$beta $=0\mathrm{.}92.$ Suppose that the S&P$500$ at the close of trading yesterday was $9,414$ and the daily volatility of the index was estimated as $2\%$ per day at that time. Assuming that the level of the index at the close of trading equals $$9,252.$

$($GARCH Model: $\backslash$sigma $\_$n$^2=\backslash$omega $+$a$*$u$\_($n$-$i$)^2+\backslash$beta $*\backslash$sigma $\_($n$-$i$)^2)$

What is the new volatility estimate?

What is the long$-$run $($average unconditional$)$ volatility of the GARCH $(1,1)$ model above? Briefly explain its meaning.