A Novel Approach to Predictive Accuracy Testing in Nested Environments

Abstract

We introduce a new approach for comparing the predictive accuracy of two nested models that bypasses the difficulties caused by the degeneracy of the asymptotic variance of forecast error loss differentials used in the construction of commonly used predictive comparison statistics. Our approach continues to rely on the out of sample MSE loss differentials between the two competing models, leads to nuisance parameter free Gaussian asymptotics and is shown to remain valid under flexible assumptions that can accommodate heteroskedasticity and the presence of mixed predictors (e.g. stationary and local to unit root). A local power analysis also establishes its ability to detect departures from the null in both stationary and persistent settings. Simulations calibrated to common economic and financial applications indicate that our methods have strong power with good size control across commonly encountered sample sizes.