Forecasting aggregate equity return volatility using crude oil price volatility: The role of nonlinearities and asymmetries

To assess the potential nonlinear predictive impact of crude oil price volatility on aggregate equity return volatility, we consider autoregressions of monthly aggregate equity return realized volatility augmented with nonlinear transformations of crude oil price realized volatility and evaluate if they improve point forecasts. Out-of-sample results based on data from 1885m1 through 1895m12 and from 1983m1 through 2017m12 illustrate that our conclusions depend heavily on the notion of forecast improvement. At the population level, the null hypothesis of no out-of-sample predictability from crude oil price realized volatility to aggregate equity return realized volatility is rejected for the linear as well as certain nonlinear specifications. On the other hand, the null hypothesis of finite-sample equal predictive ability is rejected less frequently. Among the range of models, the autoregression augmented with the one-year net crude oil price realized volatility increase is the top performer, producing statistically significant more accurate point forecasts than the benchmark.