A Markov-switching multifractal approach to forecasting realized volatility

The volatility specification of the Markov-switching Multifractal (MSM) model is proposed as an alternative mechanism for realized volatility (RV). We estimate the RV-MSM model via Generalized Method of Moments and perform forecasting by means of best linear forecasts derived via the Levinson-Durbin algorithm. The out-of-sample performance of the RV-MSM is compared against other popular time series specfications usually employed to model the dynamics of RV as well as other standard volatility models of asset returns. An intra-day data set for five major international stock market indices is used to evaluate the various models out-of-sample. We find that the RV-MSM seems to improve upon forecasts of its baseline MSM counterparts and many other volatility models in terms of mean squared errors (MSE). While the more conventional RV-ARFIMA model comes out as the most successful model (in terms of the number of cases in which it has the best forecasts for all combinations of forecast horizons and criteria), the new RV-MSM model seems often very close in its performance and in a non-negligible number of cases even dominates over the RV-ARFIMA model.