Forecasting crude oil market volatility: A Markov switching multifractal volatility approach

We use a Markov switching multifractal (MSM) volatility model to forecast crude oil return volatility. Not only can the model capture stylized facts of multiscaling, long memory, and structural breaks in volatility, it is also more parsimonious in parameterization, after allowing for hundreds of regimes in the volatility. Our in-sample results suggest that MSM models fit oil return data better than the traditional GARCH-class models. The out-of-sample results show that MSM models generate more accurate volatility forecasts than either popular GARCH-class models or the historical volatility model.