Predicting volatility based on interval regression models

Considering the inferior volatility tracking capability of the point-data-based models, we propose using the more informative price interval data and building interval regression models for volatility forecasting. To characterize the heterogeneity of the market and the nonlinearity of volatility, we incorporated the heterogeneous autoregressive structure and the Markov regime switching structure in the benchmark interval regression model, respectively, and thus propose three extended models. Our empirical examination on S&P 500 index shows that: (1) the proposed interval regression models significantly improve the volatility prediction accuracy compared to the point-data-based GARCH model. (2) Incorporating the heterogeneous structure significantly improves the volatility prediction accuracy, and the corresponding models significantly outperform the range-based ECARR model. (3) Incorporating the Markov regime switching structure improves the prediction performance, and the improvement is significant when the heterogeneous structure is characterized. The above results are robust under different market conditions, including the extremely volatile periods.