Does oil price uncertainty matter in stock market volatility forecasting?

We analyze whether oil price uncertainty and U.S. stock uncertainty can simultaneously provide additional information to volatility forecast of six major stock indexes. For model settings, we find not only the uncertainty information of previous day, but that of previous week and month will also provide incremental predictive power for the stock market volatility. Based on that, from in-sample and out-of-sample perspective, the empirical evidences imply separately incorporating oil price uncertainty into the model can significantly improve the stock market volatility forecasting performance, but the improvements vanish after controlling the effects of volatility spillover from U.S. stock market while the effect of U.S. stock uncertainty is nonnegligible and sustainable for stock volatility forecasting. We confirm this finding from average and dynamic perspective. We further proceed the process in longer-horizon volatility forecasting, the evidences cannot overturn our conclusion. This conclusion implies that we should be cautious about the stock volatility predictability based on the oil price uncertainty, which further provide some important implications for researchers, regulators and investors.