Should crude oil price volatility receive more attention than the price of crude oil? An empirical investigation via a large‐scale out‐of‐sample forecast evaluation of US macroeconomic data

Apart from the percentage change in the price of crude oil, there is a growing tradition of using various nonlinear transformations of the price of crude oil to forecast real gross domestic product growth rates, equity returns, inflation and other macroeconomic variables. This study attempts to quantify the additional potential predictive power afforded by crude oil price volatility relative to widely used crude oil price‐based variables for more than 300 US macroeconomic time series at the monthly and the quarterly sampling frequency. We observe that regressions employing crude oil price realized volatility and crude oil price realized semivolatilities tend to afford a more consistent pattern of out‐of‐sample prediction gains relative to competitors using well‐known crude oil price measures and the autoregressive benchmark at the quarterly and monthly sampling frequency. While it is somewhat harder to find evidence of finite‐sample predictive gains relative to the benchmark, the evidence is stronger with respect to population‐level predictability 1 quarter (1 month) ahead for the model with crude oil price realized semivolatilities across the considered data and models. Furthermore, point (density) forecasts employing crude oil price realized volatility tend to be more accurate than corresponding forecasts produced under the crude oil price‐based predictive regressions in a horse race.