Nonparametric Predictive Regression

Posted: 22 Sep 2012

See all articles by Ioannis Kasparis

Ioannis Kasparis

University of Cyprus - Department of Economics

Elena Andreou

University of Cyprus - Department of Economics

Peter C. B. Phillips

University of Auckland Business School; Yale University - Cowles Foundation; Singapore Management University - School of Economics

Multiple version iconThere are 2 versions of this paper

Date Written: September 21, 2012

Abstract

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 chi^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.

Keywords: Functional regression, Nonparametric predictability test, Nonparametric regression, Stock returns, Predictive regression

JEL Classification: C22, C32

Suggested Citation

Kasparis, Ioannis and Andreou, Elena and Phillips, Peter C. B., Nonparametric Predictive Regression (September 21, 2012). Cowles Foundation Discussion Paper No. 1878, Available at SSRN: https://ssrn.com/abstract=2150193

Ioannis Kasparis

University of Cyprus - Department of Economics ( email )

75 Kallipoleos Street
P.O. Box 20537
1678 Nicosia
Cyprus

Elena Andreou

University of Cyprus - Department of Economics ( email )

75 Kallipoleos Street
P.O. Box 20537
1678 Nicosia
Cyprus
+357 2 892449 (Phone)
+357 2 892432 (Fax)

Peter C. B. Phillips (Contact Author)

University of Auckland Business School ( email )

12 Grafton Rd
Private Bag 92019
Auckland, 1010
New Zealand
+64 9 373 7599 x7596 (Phone)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States
203-432-3695 (Phone)
203-432-5429 (Fax)

Singapore Management University - School of Economics

90 Stamford Road
178903
Singapore

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