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Covariance-based orthogonality tests for regressors with unknown persistence

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Author Info
Katsumi Shimotsu
Alex Maynard

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Abstract

This paper develops a new covariance-based test of orthogonality that may beattractive when regressors have roots close or equal to unity. In this case standard regression-based orthogonality tests can suffer from (i) size distortions and (ii) uncertainty regarding the appropriate model in which to frame the alternative hypothesis. The new test has good size and power against a wide range of reasonable alternatives for stationary, non-stationary, and local to unity regressors, while avoiding non-standard limiting distributions, size correction, and unit root pre-tests. Asymptotic results are derived and simulations suggest good small sample performance. As an empirical application, we test for the predictability of stock returns using two persistent regressors, the dividend-price-ratio and short-terminterest rate. The recent literature highlights the role of size distortions in traditional tests using these predictors. On the other hand, while often overturning these rejections, recently employed size-corrected regression-based tests may restrict power to alternatives that become less plausible the more persistent the regressor. The covariance-based tests, which have correct size without restricting power, also show considerably weaker evidence against orthogonality than do traditional regressions. Nevertheless, even allowing for near-unit root behavior, in many cases we still reject orthogonality at long horizons using the dividend yield and at short to medium horizons using the one-month treasury bill rate

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Publisher Info
Paper provided by Econometric Society in its series Econometric Society 2004 North American Summer Meetings with number 536.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nasm04:536

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Related research
Keywords: orthogonality; unit root; nonstationarity; long-run covariance;

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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods

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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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