Revisit the file d-gmsp9908.txt. However, we shall investigate the value of using market volatility in modeling volatility of individual stocks. Convert the two simple return series into percentage log return series.

(a) Build an AR(5)-GARCH(1,1) model with generalized error distribution for the log S\&P returns. The AR(5) contains only lags 3 and 5. Denote the fitted volatility series by spvol.

(b) Estimate a \(\operatorname{GARCH}(1,1)\) model with spvol as an exogenous variable to the \(\log\) GM return series. Check the adequacy of the model, and write down the fitted model. In S-Plus, the command is fit \(=\operatorname{garch}(g m \sim 1, \sim \operatorname{garch}(1,1)+\) spvol, cond.dist='ged')

(c) Discuss the implication of the fitted model.