Forecasting Crude Oil Volatility Using the Deep Learning-Based Hybrid Models With Common Factors

Based on empirical evidence of the Chinese commodity futures volatility dynamics, we propose a novel and flexible hybrid model, denoted as SAE-HAR-DL, which combines a supervised autoencoder (AE) with the deep learning-based HAR model framework to capture essential common factor information and uses the reconstruction error of the AE component as a regularizer to enhance the generalization ability of the testing subsample. The empirical findings strongly support the effectiveness of this model in accurately forecasting crude oil futures volatility in the post-COVID-19 era, compared to the HAR, HAR-PCA, and HAR-DL models. Moreover, a robustness check also demonstrates the positive contribution of common factors to the volatility prediction of other commodity futures. Notably, we establish that these common factors act as effective regularizers, mitigating prediction losses within the HAR model in extreme risk events such as the COVID-19 pandemic and the Russia–Ukraine conflict.