NONPARAMETRIC PREDICTIVE REGRESSION

A unifying framework for inference is developed in predictive regressions where the predictor has unknown integration properties and may be station-ary or nonstationary. Two easily implemented nonparametric F-tests are pro-posed. The test statistics are related to those of Kasparis and Phillips (2012) and are obtained by kernel regression. The limit distribution of these predic-tive tests holds for a wide range of predictors including stationary as well as non-stationary fractional and near unit root processes. In this sense the pro-posed tests provide a unifying framework for predictive inference, allowing for possibly nonlinear relationships of unknown form, and o¤ering robustness to integration order and functional form. Under the null of no predictability the limit distributions of the tests involve functionals of independent 2 variates. The tests are consistent and divergence rates are faster when the predictor is stationary. 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. Some empirical illustrations to monthly SP500 stock returns data are provided