A Nonparametric Test of the Predictive Regression Model

This article considers testing the significance of a regressor with a near unit root in a predictive regression model. The procedures discussed in this article are nonparametric, so one can test the significance of a regressor without specifying a functional form. The results are used to test the null hypothesis that the entire function takes the value of zero. We show that the standardized test has a normal distribution regardless of whether there is a near unit root in the regressor. This is in contrast to tests based on linear regression for this model where tests have a nonstandard limiting distribution that depends on nuisance parameters. Our results have practical implications in testing the significance of a regressor since there is no need to conduct pretests for a unit root in the regressor and the same procedure can be used if the regressor has a unit root or not. A Monte Carlo experiment explores the performance of the test for various levels of persistence of the regressors and for various linear and nonlinear alternatives. The test has superior performance against certain nonlinear alternatives. An application of the test applied to stock returns shows how the test can improve inference about predictability.