Understanding the conditional out-of-sample predictive impact of the price of crude oil on aggregate equity return volatility

Using monthly data from 1973 through 2020, we explore whether it is possible to improve the accuracy of one-month ahead log-aggregate equity return realized volatility point forecasts by conditioning on various nonlinear crude oil price measures widely relied on in the literature. When evaluating the evidence of unconditional relative equal predictive ability as specified in Diebold and Mariano (1995), we observe that similar to well-known economic variables, such as the dividend yield, the default yield spread and the rate of inflation, we rarely observe evidence of statistical gains in relative point forecast accuracy in favor of the crude oil price-based models. However, when evaluating the evidence of conditionalrelative equal predictive ability as specified in Giacomini and White (2006), we observe that contrary to well-known economic predictors, certain nonlinear crude oil price variables, such as the one-year net crude oil price increase suggested in Hamilton (1996) offer sizable point forecast accuracy gains relative to the benchmark. These statistical gains can also be translated into economic gains.