The file "d-hwp3dx8099.dat" contains the daily log returns of Hewlett-Packard, CRSP value-weighted index, equal-weighted index, and S\&P 500 index from 1980 to 1999. All returns are in percentages and include dividend distributions. 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 2000.

(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 S\&P 500 index returns, and (4) a fitted volatility based on a Gaussian GARCH model for the value-weighted index return. Perform a diagnostic check for the fitted models. Are the market volatility as measured by S\&P 500 index and value-weighted index returns helpful in determining the tail behavior of stock returns of Hewlett-Packard? You may choose several thresholds.