Accurate volatility forecasting in energy markets is paramount for risk management, derivative pricing, and strategic policy planning. Traditional econometric models like the Heterogeneous Auto-regressive (HAR) model effectively capture the long-memory and multi-component nature of volatility but often fail to account for non-linearities and complex, unseen dependencies. Deep learning models, particularly Long Short-Term Memory (LSTM) networks, excel at capturing these non-linear patterns but can be data-hungry and prone to overfitting, especially in noisy financial datasets. This paper proposes a novel hybrid model, HAR-LSTM-GARCH, which synergistically combines the strengths of the HAR model, an LSTM network, and a GARCH model to forecast the realized volatility of crude oil futures. The HAR component captures the persistent, multi-scale volatility dynamics, the LSTM network learns the non-linear residual patterns, and the GARCH component models the time-varying volatility of the residuals themselves. Using high-frequency data on Brent Crude futures, we compute daily Realized Volatility (RV). Our empirical results demonstrate that the proposed HAR-LSTM-GARCH model significantly outperforms the benchmark HAR, GARCH(1,1), and standalone LSTM models in both statistical accuracy and economic significance, offering a robust framework for volatility forecasting in the complex energy sector.
Romdhane et al. (Sat,) studied this question.