Working Paper: CEPR ID: DP9570
Authors: Ioannis Kasparis; Elena Andreou; Peter C. B. Phillips
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 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; Predictive Regression; Stock Returns
JEL Codes: C22; C32
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| nonparametric predictive regression tests provide a unifying framework for predictive inference (C52) | robustness to integration order and functional form under the null hypothesis of no predictability (C51) |
| nonparametric predictive regression tests provide a unifying framework for predictive inference (C52) | limit distributions of the tests are invariant to integration order (C46) |
| nonparametric predictive regression tests provide a unifying framework for predictive inference (C52) | applicable to a wide range of predictors, including stationary and nonstationary processes (C32) |
| nonparametric predictive regression tests demonstrate higher power than existing parametric tests (C52) | particularly in scenarios where deviations from unity are significant or when the predictive regression is nonlinear (C29) |
| the proposed tests are consistent (C52) | divergence rates are faster when the predictor is stationary (C22) |