Testing Predictability in the Presence of Persistent Errors

This paper considers testing predictability in predictive regression models with persistent errors. We derive limiting distributions of the ordinary least squares estimator and the corresponding Wald statistic under the condition of moderately integrated errors or local-to-unity errors. The asymptotic result establishes the connection between super-consistent estimation in correctly specified predictive regression and inconsistent estimation in spurious regression. To provide a robust test, a modification to the IVX-AR test of Yang et al. (2020) is proposed. The modified test is uniformly valid across different degrees of persistency in both predictors and errors. Simulation studies show that the new test enjoys satisfactory finite sample performances. Leveraging on the new test, we reexamine the predictive power of numerous economic variables in predicting the growth rate of the U.S. housing market, demonstrating the usefulness of the proposed test, particularly in the context of multivariate regression.