Oil Market Volatility Forecasting Under Uncertainty Theory: A Joint Modeling Framework via Uncertain Vector Autoregression

Oil price volatility forecasting remains a central challenge in financial risk management and macroeconomic policy, particularly when market uncertainty stems from expert judgment, geopolitical assessments, or imprecisely quantified fundamentals rather than statistical frequencies. We propose a bivariate uncertain vector autoregressive (UVAR) model to jointly forecast crude oil realized volatility (RV) and the Overall Equity Market Volatility (EMV) tracker within the framework of uncertainty theory, using 204 monthly observations from January 2008 to December 2024. Three cross-validation schemes consistently identify UVAR(1) as optimal, and least-squares estimation reveals an asymmetric bidirectional relationship between the two variables. Residual analysis and uncertain hypothesis testing confirm the adequacy of the fitted model at both α=0.05 and α=0.10, the conventional significance levels reported in the empirical literature. Relative to a univariate UAR benchmark, UVAR(1) yields lower residual variance and, on average, narrower 95% confidence intervals for both variables and remedies the hypothesis-test failure of UAR(1) for realized volatility; while its fixed-origin ATE is marginally higher on the EMV tracker, this is more than offset by substantial gains on realized volatility, the primary economic variable of interest. Against a probabilistic VAR(1) benchmark, UVAR(1) attains marginally lower out-of-sample sum of squared mean errors while uniquely supporting principled uncertain-statistical inference under non-frequentist data-generating mechanisms. These results provide principled inputs for value-at-risk assessment and portfolio hedging in oil-dependent economies.