Forecast the value at risk of a portfolio, assuming the portfolio logarithmic returns follow a Generalized AutoRegressive Heteroscedasticity (GARCH(1,1)) conditional variance model, coupled with an AutoRegressive Moving Average (ARMA(1,1)) conditional mean model.

References

• Christoph Hartz, Stefan Mittnik, Marc Paolella, Accurate value-at-risk forecasting based on the normal-GARCH model, Computational Statistics & Data Analysis, Volume 51, Issue 4, 2006, Pages 2295-2312
• Bollerslev, Tim, 1987. A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return, The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547