Skewness in Energy Returns : Estimation, Testing and Implications for Tail Risk

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 symmetry 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 other energy returns such as Heating oil, Kerosene and Natural gas seem to be symmetrically distributed. In addition, 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