2. 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? [Hint:if there is no serial correlation in the log returns, then use the log returns minus the sample mean to check the ARCH effect.] (b) Build a Gaussian GARCH model for the log returns. Perform model checking and write down the fitted model. [Hint: Try GARCH (1,1) and GARCH (2,1), choose the better one.] (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. [Hint: Use the same order as the chosen model in (b).] 3. Consider again the monthly log returns of KO stock. Multiple the log returns by 100. i.e., use percentage log returns. (a) Fit a TGARCH model to the series. Perform model checking and write down the fitted model. Is the leverage effect different from zero, that is whether the estimate of the parameter for asymmetry is significant? [Hint: Try Gaussian TGARCH (1,1) and Student-t TGARCH(1,1), then choose the better one.] (b) Fit a GARCH-M model to the series. Perform model checking and write down the fitted model. Is the risk premium significant? Why? [Hint: Use the volatility in mean (with ru- garch: archm=TRUE, archpow=1), instead of conditional variance in mean (archm=TRUE, archpow=2).]