Modeling the volatility of realized volatility to improve volatility forecasts in electricity markets

We use high-frequency spot prices from the Australian New South Wales (NSW) electricity market to calculate the non-parametric realized volatility as well as identify price jumps. We show that the residuals of the heterogeneous autoregressive (HAR) models of realized volatility still exhibit volatility clustering. Therefore, we extend the HAR models by characterizing such time-varying volatility of realized volatility through three GARCH-type models: the GARCH model, the long-memory FIGARCH model, and the asymmetric EGARCH model. Furthermore, we augment the above HAR-GARCH-type models to capture the inverse leverage effect and to exploit the errors in realized volatility estimators. The resulting models are referred to as the HARQ-L-GARCH-type models. They each have better in-sample fit than the corresponding HAR-GARCH-type models, whose in-sample fit are much better than the benchmark HAR models. More importantly, Diebold-Mariano tests on out-of-sample forecasts reinforce our extensions, as the forecast accuracy of the HAR-GARCH-type models significantly outperforms that of the benchmark HAR models under six conventional criteria, and the forecast accuracy of the HARQ-L-GARCH-type models is even higher. Finally, the model confidence set tests indicate that, 1) modeling the residual variance with the GARCH structure and the FIGARCH structure can more effectively improve the out-of-sample forecasting performance of the HAR models. 2) Incorporating jumps in the HAR structure improves the out-of sample forecasting performance. 3) The HARQ-L-CJ-GARCH model is superior for predicting volatility in the NSW electricity market. (C) 2018 Elsevier B.V. All rights reserved.