A Hybrid HAR-LSTM-GARCH Model for Forecasting Volatility in Energy Markets

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.