Despite its shortcoming, Value-at-Risk (VaR) remains as one of the most important measures of risk
for financial assets. Although it is used widely by regulatory authority in assessing risk of the financial markets,
the robust construction of VaR forecasts remains a controversial issue. This paper proposes a new method to
construct VaR forecasts based on Maximum Entropy Density, along with the Generalized Autoregressive
Conditional Heteroskedasticity (GARCH) model of Bollerslev (1986).
Using the result in Ling and McAleer (2003), the Quasi-Maximum Likelihood Estimator (QMLE) with the
normal density for ARMA-GARCH model is consistent and asymptotically normal under mild assumptions. This
implies that it is possible to obtain consistent estimates of the standardized residuals even when the underlying
distribution of returns is non-normal. Given this, the distribution of the standardized residuals can then be
approximated using Maximum Entropy Density (MED) which allows different

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maximum entropy　Maximum Likelihood　GARCH　
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VaR Methods——Evaluation/Comparison