Revisit the file d-gmsp9303.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 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 = garch(gm ~ 1, ~garch(1,1)+spvol, cond.dist='ged')

(c) Discuss the implication of the fitted model.