Restricted Likelihood Ratio Tests in Predictive Regression

Peter Phillips and Ye Chen
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Ye Chen: Singapore Management University

No 1968, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: Chen and Deo (2009a) proposed procedures based on restricted maximum likelihood (REML) for estimation and inference in the context of predictive regression. Their method achieves bias reduction in both estimation and inference which assists in overcoming size distortion in predictive hypothesis testing. This paper provides extensions of the REML approach to more general cases which allow for drift in the predictive regressor and multiple regressors. It is shown that without modification the REML approach is seriously oversized and can have unit rejection probability in the limit under the null when the drift in the regressor is dominant. A limit theory for the modified REML test is given under a localized drift specification that accommodates predictors with varying degrees of persistence. The extension is useful in empirical work where predictors typically involve stochastic trends with drift and where there are multiple regressors. Simulations show that with these modifications, the good performance of the restricted likelihood ratio test (RLRT) is preserved and that RLRT outperforms other predictive tests in terms of size and power even when there is no drift in the regressor.

Keywords: Localized drift; Predictive regression; Restricted likelihood ratio test; Size distortion (search for similar items in EconPapers)
JEL-codes: C12 C13 C58 (search for similar items in EconPapers)
Pages: 65 pages
New Economics Papers: this item is included in nep-ecm and nep-sea
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Citations: View citations in EconPapers (1)

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