Q$2(15$ points$)$ Consider the following first $12$ lags of sample PACF and some Information Criteria for a series of monthly stock returns from $\frac{01}{1926}$ to $\frac{12}{2008}.$ Using the $5\%$ significant level, please identify the order $p$ of AR time series. How about the answer for $1\%$ significance?

$\backslash$table$[[$p$,1,2,3,4,5,6],[$PACF$,0\mathrm{.}115,-0\mathrm{.}030,-0\mathrm{.}102,0\mathrm{.}033,0\mathrm{.}062,-0\mathrm{.}050],[$AIC$,-5\mathrm{.}838,-5\mathrm{.}837,-5\mathrm{.}846,-5\mathrm{.}845,-5\mathrm{.}847,-5\mathrm{.}847],[$BIC$,-5\mathrm{.}833,-5\mathrm{.}827,-5\mathrm{.}831,-5\mathrm{.}825,-5\mathrm{.}822,-5\mathrm{.}818],[$p$,7,8,9,10,11,12],[$PACF$,0\mathrm{.}031,0\mathrm{.}052,0\mathrm{.}063,0\mathrm{.}005,-0\mathrm{.}005,0\mathrm{.}011],[$AIC$,-5\mathrm{.}846,-5\mathrm{.}847,-5\mathrm{.}849,-5\mathrm{.}847,-5\mathrm{.}845,-5\mathrm{.}843],[$BIC$,-5\mathrm{.}812,-5\mathrm{.}807,-5\mathrm{.}805,-5\mathrm{.}798,-5\mathrm{.}791,-5\mathrm{.}784]]$