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A Fixed-b Perspective on the Phillips-Perron Unit Root Tests

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  • Vogelsang, Timothy J.

    (Department of Economics, Michigan State University, East Lansing, USA)

  • Wagner, Martin

    (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria, and Frisch Centre for Economic Research, Oslo, Norway)

Abstract

We extend fixed-b asymptotic theory to the nonparametric Phillips-Perron (PP) unit root tests. We show that the fixed-b limits depend on nuisance parameters in a complicated way. These non-pivotal limits provide an alternative theoretical explanation for the well known finite sample problems of PP tests. We also show that the fixed-b limits depend on whether deterministic trends are removed using one-step or two-step approaches, contrasting the asymptotic equivalence of the one- and two-step approaches under a consistency approximation for the long run variance estimator. Based on these results we introduce modified PP tests that allow for fixed-b inference. The theoretical analysis is cast in the framework of near-integrated processes which allows to study the asymptotic behavior both under the unit root null hypothesis as well as for local alternatives. The performance of the original and modified tests is compared by means of local asymptotic power and a small simulation study.

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File URL: http://www.ihs.ac.at/publications/eco/es-272.pdf
File Function: First version, 2011
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Bibliographic Info

Paper provided by Institute for Advanced Studies in its series Economics Series with number 272.

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Length: 19 pages
Date of creation: Jul 2011
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Handle: RePEc:ihs:ihsesp:272

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Keywords: Nonparametric kernel estimator; long run variance; detrending; one-step; two-step;

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  1. Schwert, G William, 2002. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 5-17, January.
  2. Hashimzade, Nigar & Vogelsang, Timothy, 2006. "Fixed-b Asymptotic Approximation of the Sampling Behavior of Nonparametric Spectral Density Estimators," Working Papers 06-04, Cornell University, Center for Analytic Economics.
  3. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1449-1459, December.
  4. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory for Heteroskedasticity-Autocorrelation Robust Tests," Working Papers 05-08, Cornell University, Center for Analytic Economics.
  5. Perron, Pierre & Vogelsang, Timothy J, 1992. "Testing for a Unit Root in a Time Series with a Changing Mean: Corrections and Extensions," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(4), pages 467-70, October.
  6. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-44, January.
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Cited by:
  1. Vogelsang, Timothy J. & Wagner, Martin, 2011. "Integrated Modified OLS Estimation and Fixed-b Inference for Cointegrating Regressions," Economics Series 263, Institute for Advanced Studies.

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