This paper generalizes the exponentially weighted maximum likelihood (EWML) procedure to account for volatility and higher moment dynamics of the returns distribution. Prior research uses EWML to forecast value at risk (VaR) by assuming daily equity returns following a scaled t distribution. This approach does not capture the significant degree of skewness inherent in the data, which potentially leads to an underestimation of VaR. We employ the EWML procedure to estimate a time‐varying Pearson IV distribution. Our results show that VaR forecasts based on Pearson IV using the EWML procedure are generally more accurate than those generated by scaled t and generalized autoregressive conditional heteroskedasticity (GARCH)‐type models, particularly for assets with high leptokurtosis and negative skewness.

中文翻译：

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使用条件Pearson IV型分布的动态VaR预测

本文概括了指数加权最大似然（EWML）程序，以考虑收益率分布的波动性和较高的动量动态。先前的研究使用EWML通过假设遵循按比例t分布的每日净资产收益率来预测风险价值（VaR）。这种方法不能捕获数据固有的明显偏度，这可能导致对VaR的低估。我们采用EWML程序来估计随时间变化的Pearson IV分布。我们的结果表明，使用EWML程序基于Pearson IV的VaR预测通常比按比例缩放t所生成的VaR预测更准确 以及广义自回归条件异方差（GARCH）类型的模型，尤其是对于具有高瘦度和负偏度的资产。