Uncertain HAR‐RV Models and Their Extensions: A New Perspective on Forecasting the Volatility of China's Crude Oil Futures

Traditional heterogeneous autoregressive models of realized volatility (HAR‐RV) often fail because of the invalidity of residual randomness assumptions, and limitations arise since their reliance on specific data features for volatility characterization. To address these issues, this study constructs uncertain HAR‐RV models based on uncertainty theory. Building on this foundation, this study further introduces uncertain quantiles into the modeling framework, develops uncertain quantile HAR‐RV models, and provides parameter estimation along with rigorous mathematical proofs. Finally, this study applies the constructed models to volatility forecasting in China's crude oil futures market. Through randomness tests, out‐of‐sample evaluations, and robustness tests, the limitations of traditional models that lead to failure are systematically validated, and the superior predictive performance of the proposed models across different quantiles is demonstrated. Furthermore, leveraging the unique perspective of uncertainty theory in handling imprecise data, a new perspective for volatility forecasting that uses uncertainty distributions to characterize the daily realized volatility is provided.