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Covariance-based orthogonality tests for regressors with unknown persistence

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  • Alex Maynard

    ()
    (Wilfrid Laurier University)

  • Katsumi Shimotsu

    ()
    (Queen's University)

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://qed.econ.queensu.ca/working_papers/papers/qed_wp_1122.pdf
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Bibliographic 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
Date of revision:
Handle: RePEc:qed:wpaper:1122

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

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References

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Citations

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Cited by:
  1. Yakov Amihud & Clifford Hurvich & Yi Wang, 2004. "Hypothesis Testing in Predictive Regressions," Finance 0412022, EconWPA.
  2. Jin Lee, 2012. "Nonparametric Testing for Long-Run Neutrality with Applications to US Money and Output Data," Computational Economics, Society for Computational Economics, vol. 40(2), pages 183-202, August.
  3. Paulo M.M. Rodrigues & Antonio Rubia, 2011. "A Class of Robust Tests in Augmented Predictive Regressions," Working Papers w201126, Banco de Portugal, Economics and Research Department.
  4. 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.
  5. Alex Maynard, 2006. "The forward premium anomaly: statistical artefact or economic puzzle? New evidence from robust tests," Canadian Journal of Economics, Canadian Economics Association, vol. 39(4), pages 1244-1281, November.

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