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 firstly employ the sup-Wald test to evaluate Granger causality across various quantile levels, which provides valuable information in prediction. 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 predictions indicate that the predictive effect of oil volatility on stock volatility has both positive and negative effects. In contrast, when using stock volatility as a predictor variable to forecast crude oil volatility, predictability improves relative to benchmark forecasts, particularly at more extreme quantiles. The further analysis highlights the necessity of forecast combinations to achieve an overall improvement in forecasting tasks