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A class of simple distribution-free rank-based unit root tests

  • Marc Hallin

    ()

    (Tilburg University - Tilburg University)

  • Ramon van den Akker

    ()

    (Tilburg University - Tilburg University)

  • Bas J.M. Werker

    ()

    (Tilburg University - Tilburg University)

We propose a class of distribution-free rank-based tests for the null hypothesis of a unit root. This class is indexed by the choice of a , which needs not coincide with the unknown actual innovation density . The validity of these tests, in terms of exact finite sample size, is guaranteed, irrespective of the actual underlying density, by distribution-freeness. Those tests are locally and asymptotically optimal under a particular asymptotic scheme, for which we provide a complete analysis of asymptotic relative efficiencies. Rather than asymptotic optimality, however, we emphasize finite-sample performances, which, quite heavily, also depend on initial values. It appears that our rank-based tests significantly outperform the traditional Dickey-Fuller tests, as well as the more recent procedures proposed by Elliot, Rothenberg, and Stock (1996), Ng and Perron (2001), and Elliott and Müller (2006), for a broad range of initial values and for heavy-tailed innovation densities. As such, they provide a useful complement to existing techniques.

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File URL: http://peer.ccsd.cnrs.fr/docs/00/83/44/24/PDF/PEER_stage2_10.1016%252Fj.jeconom.2011.03.007.pdf
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Paper provided by HAL in its series Post-Print with number peer-00834424.

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Date of creation: 15 Jun 2011
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Publication status: Published, Journal of Econometrics, 2011
Handle: RePEc:hal:journl:peer-00834424
Note: View the original document on HAL open archive server: http://peer.ccsd.cnrs.fr/peer-00834424
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  8. Campbell, Bryan & Dufour, Jean-Marie, 1997. "Exact Nonparametric Tests of Orthogonality and Random Walk in the Presence of a Drift Parameter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(1), pages 151-73, February.
  9. Michael Jansson, 2007. "Semiparametric Power Envelopes for Tests of the Unit Root Hypothesis," CREATES Research Papers 2007-12, School of Economics and Management, University of Aarhus.
  10. Dufour, J.M., 1981. "Rank Tests for Serial Dependence," Cahiers de recherche 8127, Universite de Montreal, Departement de sciences economiques.
  11. Campbell, Bryan & Dufour, Jean-Marie, 1995. "Exact Nonparametric Orthogonality and Random Walk Tests," The Review of Economics and Statistics, MIT Press, vol. 77(1), pages 1-16, February.
  12. Graham Elliott & Michael Jansson, . "Testing for Unit Roots with Stationary Covariates," Economics Working Papers 2000-6, School of Economics and Management, University of Aarhus.
  13. Hylleberg, Svend & Mizon, Grayham E., 1989. "A note on the distribution of the least squares estimator of a random walk with drift," Economics Letters, Elsevier, vol. 29(3), pages 225-230.
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  17. José Angel Roldán Casas & Rafaela Dios-Palomares, 2004. "A Strategy for Testing the Unit Root in AR(1) Model with Intercept. A Monte Carlo Experiment," Economic Working Papers at Centro de Estudios Andaluces E2004/37, Centro de Estudios Andaluces.
  18. Ploberger, Werner, 2008. "Admissible And Nonadmissible Tests In Unit-Root-Like Situations," Econometric Theory, Cambridge University Press, vol. 24(01), pages 15-42, February.
  19. Elliott, Graham & Muller, Ulrich K., 2006. "Minimizing the impact of the initial condition on testing for unit roots," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 285-310.
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  24. Bhargava, Alok, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," Review of Economic Studies, Wiley Blackwell, vol. 53(3), pages 369-84, July.
  25. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
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  27. Luger, Richard, 2001. "Exact Non-Parametric Tests for a Random Walk with Unknown Drift under Conditional Heteroscedasticity," Working Papers 01-2, Bank of Canada.
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  37. repec:cup:cbooks:9780521784504 is not listed on IDEAS
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