The file d-gmsp9908 . txt contains the daily simple returns of GM stock and the S&P composite index from 1999 to 2008. It has three columns denoting date, GM return, and S&P return.

(a) Compute the daily log returns of GM stock. Is there any evidence of ARCH effects in the log returns? You may use 10 lags of the squared returns and \(5 \%\) significance level to perform the test.

(b) Compute the PACF of the squared log returns (10 lags).

(c) Specify a GARCH model for the GM log return using a normal distribution for the innovations. Perform model checking and write down the fitted model.

(d) Find an adequate GARCH model for the series but using the generalized error distribution for the innovations. Write down the fitted model.