The file "m-gmsp5099.dat" contains the monthly log returns, in percentages, of General Motors stock and S\&P 500 index from 1950 to 1999. The GM stock returns are in column 1 .

- Build a GARCH model with Gaussian innovations for the log returns of GM stock. Check the model and write down the fitted model.

- Build a GARCH-M model with Gaussian innovations for the log returns of GM stock. What is the fitted model?

- Build a GARCH model with Student- \(t\) distribution with 6 degrees of freedom for the GM log returns. Check the model and write down the fitted model.

- Build a GARCH model with Student- \(t\) distribution for the log returns of GM stock, including estimation of the degrees of freedom. Write down the fitted model. Let \(v\) be the degrees of freedom of the Student- \(t\) distribution. Test the hypothesis \(H_{o}: v=6\) versus \(H_{a}: v eq 6\), using the \(5 \%\) significance level.

- Build an EGARCH model for the log returns of GM stock. What is the fitted model?

- Compare all the volatility models obtained for the log returns of GM stock. Is there any significant difference? Why?