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Covariance-Based Orthogonality Tests For Regressors With Unknown Persistence

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Author Info
Maynard, Alex
Shimotsu, Katsumi

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Abstract

This paper develops a new test of orthogonality based on a zero restriction on the covariance between the dependent variable and the predictor. The test provides a useful alternative to regression-based tests when conditioning variables have roots close or equal to unity. In this case standard predictive regression tests can suffer from well-documented size distortion. Moreover, under the alternative hypothesis, they force the dependent variable to share the same order of integration as the predictor, whereas in practice the dependent variable often appears stationary and the predictor may be near-nonstationary. By contrast, the new test does not enforce the same orders of integration and is therefore capable of detecting a rich set of alternatives to orthogonality that are excluded by the standard predictive regression model. Moreover, the test statistic has a standard normal limit distribution for both unit root and local-to-unity conditioning variables, without prior knowledge of the local-to-unity parameter. If the conditioning variable is stationary, the test remains conservative and consistent. Simulations suggest good small-sample performance. As an empirical application, we test for the predictability of stock returns using two persistent predictors, the dividend-price ratio and short-term interest rate.

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Publisher Info
Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 25 (2009)
Issue (Month): 01 (February)
Pages: 63-116
Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Handle: RePEc:cup:etheor:v:25:y:2009:i:01:p:63-116_09

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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  13. Yakov Amihud & Clifford Hurvich & Yi Wang, 2004. "Hypothesis Testing in Predictive Regressions," Finance 0412022, EconWPA. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Aaron Smallwood; Alex Maynard; Mark Wohar, 2005. "The Long and the Short of It: Long Memory Regressors and Predictive Regressions," Computing in Economics and Finance 2005 384, Society for Computational Economics. [Downloadable!]
  2. Yakov Amihud & Clifford Hurvich & Yi Wang, 2004. "Hypothesis Testing in Predictive Regressions," Finance 0412022, EconWPA. [Downloadable!]
  3. Wei Liu & Alex Maynard, 2007. "A New Application of Exact Nonparametric Methods to Long-Horizon Predictability Tests," Studies in Nonlinear Dynamics & Econometrics, Berkeley Electronic Press, vol. 11(1), pages 1376-1376. [Downloadable!] (restricted)
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