Bias Reduction and Likelihood Based Almost-Exactly Sized Hypothesis Testing in Predictive Regressions Using the Restricted Likelihood

46 Pages Posted: 27 Sep 2006 Last revised: 2 Jun 2009

See all articles by Willa W. Chen

Willa W. Chen

Texas A&M University - Department of Statistics

Rohit Deo

Stern School of Business, New York University

Date Written: July 5, 2008

Abstract

Abstract: Difficulties with inference in predictive regressions are generally attributed to strong persistence in the predictor series. We show that the major source of the problem is actually the nuisance intercept parameter and propose basing inference on the Restricted Likelihood, which is free of such nuisance location parameters and also possesses small curvature, making it suitable for inference. The bias of the Restricted Maximum Likelihood (REML) estimates is shown to be approximately 50% less than that of the OLS estimates near the unit root, without loss of eýciency. The error in the chi-square approximation to the distribution of the REML based Likelihood Ratio Test (RLRT) for no predictability is shown to be (3/4-rho^2)n^-1 (G3 (x) -G1 (x)) O(n^-2); where rho < 1 is the correlation of the innovation series and Gs (x) is the c.d.f. of a chi-sq random variable. This very small error, free of the AR parameter, suggests that the RLRT for predictability has very good size properties even when the regressor has strong persistence. The Bartlett corrected RLRT achieves an O(n^-2) error.

Power under local alternatives is obtained and extensions to more general univariate regressors and vector AR(1) regressors, where OLS may no longer be asymptotically efficient, are provided. In simulations the RLRT maintains size well, is robust to non-normal errors and has uniformly higher power than the Jansson-Moreira test with gains that can be substantial. The Campbell-Yogo Bonferroni Q test is found to have size distortions and can be signicantly oversized.

Keywords: Bartlett Correction, Likelihood Ratio Test, Curvature

JEL Classification: C12, C13

Suggested Citation

Chen, Willa W. and Deo, Rohit, Bias Reduction and Likelihood Based Almost-Exactly Sized Hypothesis Testing in Predictive Regressions Using the Restricted Likelihood (July 5, 2008). Available at SSRN: https://ssrn.com/abstract=932996 or http://dx.doi.org/10.2139/ssrn.932996

Willa W. Chen

Texas A&M University - Department of Statistics ( email )

155 Ireland Street
447 Blocker
College Station, TX 77843
United States

Rohit Deo (Contact Author)

Stern School of Business, New York University ( email )

44 West Fourth Street
New York, NY 10012
United States

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