The file d-csco9199.txt contains the daily simple returns of Cisco Systems stock from 1991 to 1999 with 2275 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 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.