This paper investigates the time-varying conditional higher moments of the daily returns on WTI crude oil futures, using the GJR-GARCH model with Gram-Charlier expansion (GCE) of normal density. The empirical results suggest significant time-variations in the conditional skewness and kurtosis. The out-of-sample value-at-risk (VaR) forecasting results show the advantage of models with dynamic higher moments over those with constant higher moments.
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Huang, Z., Liang, F., Wang, T., & Li, C. (2021). Modeling dynamic higher moments of crude oil futures. Finance Research Letters, 39, 101570. https://doi.org/10.1016/j.frl.2020.101570