Forecasting stock market in high and low volatility periods: a modified multifractal volatility approach

We propose a new multifractal volatility measure (MVA) and accordingly construct new types of multifractal volatility models. We compare these models to some alternatives, and consider long memory features, the benefits of leverage effects, and the presence of jumps. The analysis is applied to the multifractal volatility and realized volatility series of three representative indices, adopting six loss functions as guidance for the model selection. The forecast performance is evaluated and tested using model confident set (MCS) in both high- and low-volatility periods, as well as based on robustness checks on the continuous rank probability score statistics. The results show satisfactory performances for the new multifractal volatility models. Specifically, we find that our new multifractal volatility model significantly improves the one-day-ahead volatility forecasts in the high-volatility period. While in the low-volatility periods, the out-of-sample test results highlight the superiority of the traditional multifractal volatility models in the accuracy of volatility forecasting. These findings will be helpful for market volatility prediction and investment strategies.