Consider the monthly stock returns of the Coca-Cola Company (KO) from January 1961 to September 2011. The simple returns are available from CRSP and in the file m-ko-6111.txt. Transform the simple returns to log returns.

(a) Is the expected monthly log return zero? Is there any serial correlation in the log returns? Is there any ARCH effect in the log returns?

(b) Build a Gaussian GARCH model for the log returns. Perform model checking and write down the fitted model.

(c) Build a GARCH model with Student \(t\) innovations for the log returns. Perform model checking, obtain the QQ plot of the standardized residuals, and write down the fitted model. Also, obtain 1- to 5 -step ahead volatility predictions.