We expand the literature of volatility and Value-at-Risk forecasting of oil price returns by comparing the recently proposed Mixture Memory GARCH (MMGARCH) model to other discrete volatility models (GARCH, RiskMetrics, EGARCH, APARCH, FIGARCH, HYGARCH, and FIAPARCH). We incorporate an Expectation-Maximization algorithm for parameter estimation of the MMGARCH and find different structures in volatility level as well as shock persistence. MMGARCH is also able to cover asymmetric and long memory effects. Furthermore, a dissimilar memory structure in variance of WTI and Brent crude oil prices is observed which is supported by additional tests. Parameter estimation and comparison of the models reveal significant long memory and asymmetry in oil price returns. In regard of variance forecasting and Value-at-Risk prediction, it is shown that MMGARCH outperforms the aforementioned models due to its dynamic approach in varying the volatility level and memory of the process. We find MMGARCH superior for application in risk management as a result of its flexibility in adjusting to variance shifts and shocks.
Klein, T., & Walther, T. (2016). Oil price volatility forecast with mixture memory GARCH. Energy Economics, 58, 46–58. https://doi.org/10.1016/j.eneco.2016.06.004