Does crude oil futures price really help to predict spot oil price? New evidence from density forecasting

In this paper, we detect the contributions of various predictors in terms of density forecasts of monthly West Texas Intermediate (WTI) crude oil prices. In the first step, we use a simple predictive regression of crude oil prices on different predictors one‐by‐one as explanatory variables, and then two kinds of criteria, Log Score and Continuous Ranked Probability Score (CRPS), are employed to evaluate the density forecasting accuracy of them. In the second step, we utilize a CRPS‐weighted combination and an equal‐weighted combination, respectively, to assemble various density forecasting results in the first step. Finally, a novel test proposed by Rossi and Sekhposyan (2019) is adopted to verify the correct calibration of predictive densities by these two combination methods as well as an AR benchmark model. The empirical results indicate that those predictors proved to perform well (poor) in point forecasts of crude oil price in extant literature do not necessarily offer high (low) density forecasting accuracy. Interestingly, WTI oil futures price is the only predictor that can produce good out‐of‐sample density forecasts across various time horizons. In addition, we find that the two model combination methods can beat the AR benchmark in density forecasting of crude oil price. However, no model can produce correct calibration of predictive densities for crude oil price at time horizons longer than about 5 years.