IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://peer.ccsd.cnrs.fr/docs/00/83/44/24/PDF/PEER_stage2_10.1016%252Fj.jeconom.2011.03.007.pdf
Download Restriction: no

Paper provided by HAL in its series Post-Print with number peer-00834424.

as
in new window

Length:
Date of creation: 15 Jun 2011
Date of revision:
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
Contact details of provider: Web page: http://hal.archives-ouvertes.fr/

References listed on IDEAS
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.:

as in new window
  1. Thompson, Samuel B., 2004. "Optimal Versus Robust Inference In Nearly Integrated Non-Gaussian Models," Econometric Theory, Cambridge University Press, vol. 20(01), pages 23-55, February.
  2. 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.
  3. 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.
  4. Dufour, J.M. & Campbell, B., 1993. "Exact Nonparametric Orthogonality and Random Walk Tests," Cahiers de recherche 9326, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  5. Elliott, Graham & Jansson, Michael, 2000. "Testing for Unit Roots with Stationary Covariances," University of California at San Diego, Economics Working Paper Series qt47k7z69n, Department of Economics, UC San Diego.
  6. Dufour, J.M., 1981. "Rank Tests for Serial Dependence," Cahiers de recherche 8127, Universite de Montreal, Departement de sciences economiques.
  7. Serena Ng & Pierre Perron, 1997. "Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power," Boston College Working Papers in Economics 369, Boston College Department of Economics, revised 01 Sep 2000.
  8. Ulrich K. M¸ller & Graham Elliott, 2003. "Tests for Unit Roots and the Initial Condition," Econometrica, Econometric Society, vol. 71(4), pages 1269-1286, 07.
  9. 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.
  10. 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.
  11. Michael Jansson, 2008. "Semiparametric Power Envelopes for Tests of the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 76(5), pages 1103-1142, 09.
  12. Drost, F.C. & Klaassen, C.A.J. & Werker, B.J.M., 1997. "Adaptive estimation in time-series models," Other publications TiSEM aa253902-af93-4e1e-b974-2, Tilburg University, School of Economics and Management.
  13. Werner Ploberger, 2004. "Admissible and Nonadmissible Test in Unit-Root-like Situations," Econometric Society 2004 North American Summer Meetings 555, Econometric Society.
  14. Elise Coudin & Jean-Marie Dufour, 2007. "Finite-sample Distribution-free Inference in Linear Median Regression under Heteroskedasticity and Nonlinear Dependence of Unknown Form," Working Papers 2007-38, Centre de Recherche en Economie et Statistique.
  15. Perron, Pierre, 1988. "Trends and random walks in macroeconomic time series : Further evidence from a new approach," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 297-332.
  16. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
  17. Levin, Andrew & Lin, Chien-Fu & James Chu, Chia-Shang, 2002. "Unit root tests in panel data: asymptotic and finite-sample properties," Journal of Econometrics, Elsevier, vol. 108(1), pages 1-24, May.
  18. Michael Jansson & Marcelo J. Moreira, 2004. "Optimal Inference in Regression Models with Nearly Integrated Regressors," Harvard Institute of Economic Research Working Papers 2047, Harvard - Institute of Economic Research.
  19. 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, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  20. Ploberger, Werner, 2004. "A complete class of tests when the likelihood is locally asymptotically quadratic," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 67-94.
  21. repec:cup:cbooks:9780521784504 is not listed on IDEAS
  22. Marc Hallin & Yvik Swan & Thomas Verdebout & David Veredas, 2011. "Rank-based testing in linear models with stable errors," ULB Institutional Repository 2013/136196, ULB -- Universite Libre de Bruxelles.
  23. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
  24. Graham Elliott & Thomas J. Rothenberg & James H. Stock, 1992. "Efficient Tests for an Autoregressive Unit Root," NBER Technical Working Papers 0130, National Bureau of Economic Research, Inc.
  25. Thompson, Samuel B., 2004. "Robust Tests Of The Unit Root Hypothesis Should Not Be," Econometric Theory, Cambridge University Press, vol. 20(02), pages 360-381, April.
  26. 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.
  27. Rothenberg, Thomas J. & Stock, James H., 1997. "Inference in a nearly integrated autoregressive model with nonnormal innovations," Journal of Econometrics, Elsevier, vol. 80(2), pages 269-286, October.
  28. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  29. Jeganathan, P., 1995. "Some Aspects of Asymptotic Theory with Applications to Time Series Models," Econometric Theory, Cambridge University Press, vol. 11(05), pages 818-887, October.
  30. Pasaran, M.H. & Im, K.S. & Shin, Y., 1995. "Testing for Unit Roots in Heterogeneous Panels," Cambridge Working Papers in Economics 9526, Faculty of Economics, University of Cambridge.
  31. Luger, Richard, 2001. "Exact Non-Parametric Tests for a Random Walk with Unknown Drift under Conditional Heteroscedasticity," Working Papers 01-2, Bank of Canada.
  32. Hasan, Mohammad N., 2001. "Rank tests of unit root hypothesis with infinite variance errors," Journal of Econometrics, Elsevier, vol. 104(1), pages 49-65, August.
  33. 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.
  34. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
  35. Sung Ahn & Stergios Fotopoulos & Lijian He, 2001. "Unit Root Tests With Infinite Variance Errors," Econometric Reviews, Taylor & Francis Journals, vol. 20(4), pages 461-483.
  36. M. N. Hasan & R. W. Koenker, 1997. "Robust Rank Tests of the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 65(1), pages 133-162, January.
  37. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November.
  38. West, Kenneth D, 1988. "Asymptotic Normality, When Regressors Have a Unit Root," Econometrica, Econometric Society, vol. 56(6), pages 1397-1417, November.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:hal:journl:peer-00834424. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.