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Covariance-based orthogonality tests for regressors with unknown persistence

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Author Info
Alex Maynard () (Wilfrid Laurier University)
Katsumi Shimotsu () (Queen's University)

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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 while 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 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. Thus the new test requires neither size correction nor unit root pre-test. 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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File URL: http://www.econ.queensu.ca/working_papers/papers/qed_wp_1122.pdf
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Publisher Info
Paper provided by Queen's University, Department of Economics in its series Working Papers with number 1122.

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Length: 53 pages
Date of creation: Feb 2007
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Handle: RePEc:qed:wpaper:1122

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Related research
Keywords: orthogonality test covariance estimation local-to-unity unit roots market efficiency predictive regression regression imbalance

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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models

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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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  6. Andrew Ang & Geert Bekaert, 2001. "Stock Return Predictability: Is it There?," NBER Working Papers 8207, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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Full references

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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