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A class of Simple Semiparametrically Efficient Rank-Based Unit Root Tests

  • Marc Hallin
  • Ramon van den Akker
  • Bas Werker

We propose a class of simple rank-based tests for the null hypothesis of a unit root. This class is indexed by the choice of a reference density g, which needs not coincide with the unknown actual innovation density f. The validity of these tests, in terms of exact finite sample size, is guaranteed by distribution-freeness, irrespective of the value of the drift and the actual underlying f. When based on a Gaussian reference density g, our tests (of the van der Waerden form) perform uniformly better, in terms of asymptotic relative effciency, than the Dickey and Fuller test --except under Gaussian f, where they are doing equally well. Under Student t3 density f, the effciency gain is as high as 110%, meaning that Dickey-Fuller requires over twice as many observations as we do in order to achieve comparable performance. This gain is even larger in case the underlying f has fatter tails; under Cauchy f, where Dickey and Fuller is no longer valid, it can be considered infinite. The test associated with reference density g is semiparametrically e±cient when f happens to coincide with g, in the ubiquitous case that the model contains a non-zero drift. Finally, with an estimated density f(n) substituted for the reference density g, our tests achieve uniform (with respect to f) semiparametric efficiency.

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Paper provided by ULB -- Universite Libre de Bruxelles in its series Working Papers ECARES with number 2009_001.

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Length: 23 p.
Date of creation: 2009
Date of revision:
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Handle: RePEc:eca:wpaper:2009_001
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  8. Campbell, B. & Dufour, J.M., 1994. "Excat Nonparametric Tests of Orthogonality and Random Walk in the Presence of a Drift Parameter," Cahiers de recherche 9407, Universite de Montreal, Departement de sciences economiques.
  9. 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.
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  15. Drost, F.C. & Klaasens, C.A.J. & Werker, B.J.M., 1994. "Adaptive Estimation in Time Series Models," Papers 9488, Tilburg - Center for Economic Research.
  16. Breitung, Jörg & Gouriéroux, Christian, 1996. "Rank tests for unit roots," SFB 373 Discussion Papers 1996,9, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  17. 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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  20. 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.
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