Consider the daily log returns of GE stock from July 3, 1962 to December 31, 1999. The data can be obtained from CRSP or the file "d-geln.dat." Suppose that you hold a long position on the stock valued at \(\$ 1\) million. Use the tail probability 0.05 . Compute the value at risk of your position for 1-day horizon and 15-day horizon using the following methods:

(a) The RiskMetrics method.

(b) A Gaussian ARMA-GARCH model.

(c) An ARMA-GARCH model with a Student-t distribution. You should also estimate the degrees of freedom.

(d) The traditional extreme value theory with subperiod length \(n=21\).