We provide evidence suggesting that the assumption on the probability distribution for return innovations is more influential for Value at Risk (VaR) performance than the conditional volatility specification. We also show that some recently proposed asymmetric probability distributions and the APARCH and FGARCH volatility specifications beat more standard alternatives for VaR fore- casting, and they should be preferred when estimating tail risk. The flexibility of the free power parameter in conditional volatility in the APARCH and FGARCH models explains their better performance. Indeed, our estimates suggest that for a number of financial assets, the dynamics of volatility should be specified in terms of the conditional standarddeviation. Wedrawourresults on VaRforecastingperformance fromi) a variety of back testing approaches, ii) the Model Confidence Set approach, as well as iii) establishing a ranking among alternative VaR models using a precedence criterion that we introduceinthispaper.

中文翻译：

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VaR 预测中的波动率规范与概率分布

我们提供的证据表明，与条件波动率规范相比，关于回报创新概率分布的假设对风险价值 (VaR) 表现的影响更大。我们还表明，最近提出的一些非对称概率分布以及 APARCH 和 FGARCH 波动率规范优于 VaR 预测的更多标准替代方案，并且在估计尾部风险时应该首选它们。APARCH 和 FGARCH 模型中条件波动的自由功率参数的灵活性解释了它们更好的性能。事实上，我们的估计表明，对于许多金融资产，波动性的动态应该根据条件标准偏差来指定。我们从 i) 各种回溯测试方法中得出有关 VaRforecastingperformance 的结果，