Nonparametric predictive regression

A unifying framework for inference is developed in predictive regressions where the predictor has unknown integration properties and may be stationary or nonstationary. Two easily implemented nonparametric F-tests are proposed. The limit distribution of these predictive tests is nuisance parameter free and holds for a wide range of predictors including stationary as well as non-stationary fractional and near unit root processes. Asymptotic theory and simulations show that the proposed tests are more powerful than existing parametric predictability tests when deviations from unity are large or the predictive regression is nonlinear. Empirical illustrations to monthly SP500 stock returns data are provided.