Forecasting the volatility of WTI crude oil futures: a new perspective from uncertain threshold HAR models

The threshold heterogeneous autoregressive (THAR) model, by introducing a threshold mechanism, partitions volatility into different intervals, especially providing more refined treatment for extreme volatility parts, thereby compensating to some extent for the deficiencies of the traditional HAR model. However, in the complex and ever-changing financial market environment, the assumption of random residuals in the traditional THAR model often fails to hold, which significantly restricts the model’s applicability. Moreover, the model mainly relies on specific data characteristics to depict volatility while neglecting the intrinsic structure of the data, which, to some degree, weakens the model’s predictive accuracy and stability. To overcome the aforementioned issues, this paper constructs two uncertain THAR models based on uncertainty theory: one is the uncertain THAR model based on uncertain residuals (UR-UTHAR), and the other is the uncertain THAR model under imprecise data conditions (UV-UTHAR). Corresponding parameter estimations for these models are also provided. This paper takes the volatility of WTI crude oil futures as the research object for volatility prediction. By employing three randomness testing methods, this paper comprehensively verifies the limitations of the traditional THAR model in complex market environments. Meanwhile, using various out-of-sample evaluation methods, the significant advantages of the proposed models over traditional models in terms of predictive accuracy and stability are further demonstrated. Finally, by investigating the applicability of the models under three major event shocks: the global financial crisis, international crude oil price shocks, and the COVID-19 pandemic, the above conclusions are further consolidated, proving the robustness and effectiveness of the proposed models under different conditions.