COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1878 Nonparametric Predictive Regression Ioannis Kasparis, Elena Andreou, and Peter C.B. Phillips September 2012 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 test
statistics are related to those of Kasparis and Phillips (2012) and are obtained by kernel
regression. The limit distribution of these predictive 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 proposed tests provide a unifying framework for predictive
inference, allowing for possibly nonlinear relationships of unknown form, and offering
robustness to integration order and functional form. Under the null of no predictability
the limit distributions of the tests involve functionals of independent chi2
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. |
