The file d-hpq3dx9808. txt contains dates and the daily simple returns of Hewlett-Packard, the CRSP value-weighted index, equal-weighted index, and the S\&P 500 index from 1998 to 2008. The returns include dividend distributions. Transform the simple returns to log returns. Assume that the tail probability of interest is 0.01 . Calculate value at risk for the following financial positions for the first trading day of year 2009.

(a) Long on Hewlett-Packard stock of \(\$ 1\) million and S&P 500 index of \(\$ 1\) million using RiskMetrics. The \(\alpha\) coefficient of the \(\operatorname{IGARCH}(1,1)\) model for each series should be estimated.

(b) The same position as part (a) but using a univariate ARMA-GARCH model for each return series.

(c) A long position on Hewlett-Packard stock of \(\$ 1\) million using a twodimensional nonhomogeneous Poisson model with the following explanatory variables: (1) an annual time trend, (2) a fitted volatility based on a Gaussian GARCH model for Hewlett-Packard stock, (3) a fitted volatility based on a Gaussian GARCH model for the S&P 500 index returns, and (4) a fitted volatility based on a Gaussian GARCH model for the valueweighted index return. Perform a diagnostic check for the fitted models. Are the market volatility as measured by the S&P 500 index and valueweighted index returns helpful in determining the tail behavior of stock returns of Hewlett-Packard? You may choose several thresholds.