In this paper we estimate the skewness of the unconditional distribution of energy returns and test its statistical significance. We compare the performance of traditional and robust tests for skewness with those based on the implied unconditional skewness in a TGARCH model with Gram-Charlier (TGARCH-GC) innovations. We also analyze the implications of TGARCH-GC skewness for tail risk through evaluation of Value-at-Risk (VaR) and expected shortfall (ES) accuracy. Our results show that crude oil (Brent and WTI) and Gasoline returns are negatively skewed, while we do not find evidence of skewed distribution for other energy returns such as Heating oil, Kerosene and Natural gas. This indicates that the returns of the former are likely to encapsulate more largely the effect of negative shocks and so present higher tail risk than those of the latter. These results differ from traditional and robust tests for skewness providing important information on how to improve mean-variance risk management measures. Indeed, we find that the three-moment VaR and ES measures based on the third-order Cornish Fisher (CF3) expansion for the unconditional distribution of returns considerably improve their corresponding two-moment ones. We adopt CF3 to disentangle skewness effects from kurtosis in tail risk.

在本文中，我们估计了能量回报无条件分布的偏度并检验了其统计显着性。我们将传统稳健偏度测试的性能与基于具有 Gram-Charlier (TGARCH-GC) 创新的 TGARCH 模型中隐含无条件偏度的测试进行了比较。我们还通过评估风险价值 (VaR) 和预期缺口 (ES) 准确性来分析 TGARCH-GC 偏度对尾部风险的影响。我们的结果表明，原油（布伦特和 WTI）和汽油回报呈负偏态，而我们没有发现其他能源回报（例如取暖油、煤油和天然气）存在偏态分布的证据。这表明前者的回报可能更多地体现了负面冲击的影响，因此比后者的尾部风险更高。这些结果不同于传统的稳健偏度检验，提供了有关如何改进均值方差风险管理措施的重要信息。事实上，我们发现基于无条件回报分布的三阶 Cornish Fisher (CF3) 展开式的三矩 VaR 和 ES 度量显着改善了相应的两矩 VaR 和 ES 度量。我们采用 CF3 来消除尾部风险峰度的偏度影响。