Forecasting crude oil price returns: Can nonlinearity help?

The nonlinear components of predictors could be informative, while conventional predictive regression models only consider the linear components in the time-series prediction of crude oil price returns. Inspired by this, we propose a novel method to obtain useful information embedded in the predictors’ nonlinearity. We incorporate not only the original predictors (i.e., the linear components) but also their quadratic terms (i.e., the nonlinear components) when generating diffusion indices. The diffusion indices with nonlinearity can improve the crude oil return predictability both in- and out-of-sample. We also consider alternative nonlinear measures, including exponential, absolute, higher-power, and interactive forms. The loading results with supervised learning suggest that squared-form variables are informative. Furthermore, the diffusion indices with nonlinearity are better equipped to explain the supply and demand of crude oil, which is the economic source of predictability. The predictability is also significant in a market-timing exercise and survives a series of robustness checks and extensions.