The file d-csco9808. txt contains the daily simple returns of Cisco Systems stock from 1998 to 2008 with 2767 observations. Transform the simple returns to \(\log\) returns. Suppose that you hold a long position of Cisco stock valued at \(\$ 1\) million. Compute the value at risk of your position for the next trading day using probability \(p=0.01\).

(a) Use the RiskMetrics method.

(b) Use a GARCH model with a conditional Gaussian distribution.

(c) Use a GARCH model with a Student- \(t\) distribution. You may also estimate the degrees of freedom.

(d) Use the unconditional sample quantile.

(e) Use a two-dimensional homogeneous Poisson process with threshold 2%, that is, focusing on the exceeding times and exceedances that the daily stock price drops \(2 \%\) or more. Check the fitted model.

(f) Use a two-dimensional nonhomogeneous Poisson process with threshold \(2 \%\). The explanatory variables are (1) an annual time trend, (2) a dummy variable for October, November, and December, and (3) a fitted volatility based on a Gaussian \(\operatorname{GARCH}(1,1)\) model. Perform a diagnostic check on the fitted model.

(g) Repeat the prior two-dimensional nonhomogeneous Poisson process with threshold 2.5 or \(3 \%\). Comment on the selection of threshold.