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Covariance-Based Orthogonality Tests For Regressors With Unknown Persistence

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  • Maynard, Alex
  • Shimotsu, Katsumi

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.

Suggested Citation

  • Maynard, Alex & Shimotsu, Katsumi, 2009. "Covariance-Based Orthogonality Tests For Regressors With Unknown Persistence," Econometric Theory, Cambridge University Press, vol. 25(01), pages 63-116, February.
  • Handle: RePEc:cup:etheor:v:25:y:2009:i:01:p:63-116_09
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    Cited by:

    1. Yakov Amihud & Clifford Hurvich & Yi Wang, 2004. "Hypothesis Testing in Predictive Regressions," Finance 0412022, EconWPA.
    2. Paulo M.M. Rodrigues & Matei Demetrescu, 2016. "Residual-augmented IVX predictive regression," Working Papers w201605, Banco de Portugal, Economics and Research Department.
    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. Jin Lee, 2012. "Nonparametric Testing for Long-Run Neutrality with Applications to US Money and Output Data," Computational Economics, Springer;Society for Computational Economics, vol. 40(2), pages 183-202, August.
    5. Breitung, Jörg & Demetrescu, Matei, 2015. "Instrumental variable and variable addition based inference in predictive regressions," Journal of Econometrics, Elsevier, vol. 187(1), pages 358-375.
    6. 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.
    7. 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.

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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