This paper uses the Markov-switching multifractal (MSM) model and generalized autoregressive conditional heteroscedasticity (GARCH)-type models to forecast oil price volatility over the time periods from January 02, 1875 to December 31, 1895 and from January 03, 1977 to March 24, 2014. Based on six different loss functions and by means of the superior predictive ability (SPA) test, we evaluate and compare their forecasting performance at short and long horizons. The empirical results indicate that none of our volatility models can uniformly outperform other models across all six different loss functions. However, the new MSM model comes out as the model that most often across forecasting horizons and subsamples cannot be outperformed by other models, with long memory GARCH-type models coming out second best.
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