BIAS REDUCTION AND LIKELIHOOD-BASED ALMOST EXACTLY SIZED HYPOTHESIS TESTING IN PREDICTIVE REGRESSIONS USING THE RESTRICTED LIKELIHOOD

Willa W. Chen and Rohit Deo ()

Econometric Theory, 2009, vol. 25, issue 5, 1143-1179

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 we 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 ordinary least squares (OLS) estimates near the unit root, without loss of efficiency. 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 $({\textstyle{3 \over 4}} - \rho ^2)n^{ - 1} (G_3 (\cdot) - G_1 (\cdot)) + O(n^{ - 2}),$ where |ρ|

Date: 2009
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