Forecasting crude oil volatility and stock volatility: New evidence from the quantile autoregressive model

This paper employs the quantile autoregressive (QAR) model to examine the forecasting relationship between stock volatility and crude oil volatility. We first utilize the sup-Wald test to evaluate Granger causality across various quantile levels, providing valuable information for forecasting. Our findings reveal that the causal effects between stock volatility and crude oil volatility differ considerably across different quantiles, with a V-shaped relationship evident at the quantile level. Results from out-of-sample forecasts indicate that the forecasting effect of oil volatility on stock volatility has both positive and negative impacts. In contrast, when using stock volatility to forecast crude oil volatility, predictability improves relative to the benchmark, particularly at more extreme quantiles. Further analysis highlights the necessity of forecast combinations to achieve an overall improvement in forecasting tasks.