IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article

Residuals-based tests for the null of no-cointegration: an Analytical comparison

  • Elena Pesavento

This article studies the asymptotic distribution of five residuals-based tests for the null of no-cointegration under a local alternative when the tests are computed using both ordinary least squares (OLS) and generalized least squares (GLS)-detrended variables. The local asymptotic power of the tests is shown to be a function of Brownian motion and Ornstein-Uhlenbeck processes, depending on a single nuisance parameter, which is determined by the correlation at frequency zero of the errors of the cointegration regression with the shocks to the right-hand side variables. The tests are compared in terms of power in large and small samples. It is shown that, while no significant improvement can be achieved by using unit root tests other than the OLS detrended t-test originally proposed by Engle and Granger (1987), the power of GLS residuals tests can be higher than the power of system tests for some values of the nuisance parameter. Copyright 2007 The Author Journal compilation 2007 Blackwell Publishing Ltd.

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://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9892.2006.00501.x
File Function: link to full text
Download Restriction: Access to full text is restricted to subscribers.

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Wiley Blackwell in its journal Journal of Time Series Analysis.

Volume (Year): 28 (2007)
Issue (Month): 1 (01)
Pages: 111-137

as
in new window

Handle: RePEc:bla:jtsera:v:28:y:2007:i:1:p:111-137
Contact details of provider: Web page: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782

Order Information: Web: http://www.blackwellpublishing.com/subs.asp?ref=0143-9782

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. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, May.
  2. Peter C.B. Phillips, 1986. "Towards a Unified Asymptotic Theory for Autoregression," Cowles Foundation Discussion Papers 782R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1986.
  3. Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 1," Cowles Foundation Discussion Papers 811R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1987.
  4. Pesavento, Elena, 2000. "Analytical Evaluation of the Power of Tests for the Absence of Cointegration," University of California at San Diego, Economics Working Paper Series qt4cq4773c, Department of Economics, UC San Diego.
  5. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
  6. Peter Boswijk, H., 1994. "Testing for an unstable root in conditional and structural error correction models," Journal of Econometrics, Elsevier, vol. 63(1), pages 37-60, July.
  7. Ng, S. & Perron, P., 1994. "Unit Root Tests ARMA Models with Data Dependent Methods for the Selection of the Truncation Lag," Cahiers de recherche 9423, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  8. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
  9. Peter C. B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-470, December.
  10. Jeremy Berkowitz & Lutz Kilian, 2000. "Recent developments in bootstrapping time series," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 1-48.
  11. Swensen, Anders Rygh, 2003. "A Note On The Power Of Bootstrap Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 19(01), pages 32-48, February.
  12. Peter C.B. Phillips, 1985. "Understanding Spurious Regressions in Econometrics," Cowles Foundation Discussion Papers 757, Cowles Foundation for Research in Economics, Yale University.
  13. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  14. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-93, January.
  15. Bruce E. Hansen, 1995. "Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power," Boston College Working Papers in Economics 300., Boston College Department of Economics.
  16. Kremers, Jeroen J M & Ericsson, Neil R & Dolado, Juan J, 1992. "The Power of Cointegration Tests," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 325-48, August.
  17. Banerjee, Anindya, et al, 1986. "Exploring Equilibrium Relationships in Econometrics through Static Models: Some Monte Carlo Evidence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 253-77, August.
  18. Phillips, Peter C B, 1988. "Regression Theory for Near-Integrated Time Series," Econometrica, Econometric Society, vol. 56(5), pages 1021-43, September.
  19. Haug, A.A., 1992. "Tests for Cointegration: A Monte Carlo Comparison," Papers 93-2, York (Canada) - Department of Economics.
  20. Graham Elliott & Michael Jansson & Elena Pesavento, 2005. "Optimal Power for Testing Potential Cointegrating Vectors With Known Parameters for Nonstationarity," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 34-48, January.
  21. Atsushi Inoue & Lutz Kilian, 2000. "Bootstrapping Autoregressive Processes with Possible Unit Roots," Econometric Society World Congress 2000 Contributed Papers 0401, Econometric Society.
  22. Neil R. Ericsson & James G. MacKinnon, 1999. "Distributions of error correction tests for cointegration," International Finance Discussion Papers 655, Board of Governors of the Federal Reserve System (U.S.).
  23. Ronald Bewley & Minxian Yang, 1998. "On The Size And Power Of System Tests For Cointegration," The Review of Economics and Statistics, MIT Press, vol. 80(4), pages 675-679, November.
  24. Gonzalo, J. & Lee, T.H., 1995. "Pitfalls in Testing for Long Run Relationships," Papers 38, Boston University - Department of Economics.
  25. Hansen, Bruce E., 1992. "Efficient estimation and testing of cointegrating vectors in the presence of deterministic trends," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 87-121.
  26. Engle, Robert F. & Yoo, Byung Sam, 1987. "Forecasting and testing in co-integrated systems," Journal of Econometrics, Elsevier, vol. 35(1), pages 143-159, May.
  27. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-36, July.
  28. Graham Elliott & Michael Jansson, . "Testing for Unit Roots with Stationary Covariates," Economics Working Papers 2000-6, Department of Economics and Business Economics, Aarhus University.
  29. Chang, Yoosoon & Park, Joon Y. & Song, Kevin, 2006. "Bootstrapping cointegrating regressions," Journal of Econometrics, Elsevier, vol. 133(2), pages 703-739, August.
  30. Haug, Alfred A., 1993. "Residual based tests for cointegration : A Monte Carlo study of size distortions," Economics Letters, Elsevier, vol. 41(4), pages 345-351.
  31. Li, Hongyi & Maddala, G. S., 1997. "Bootstrapping cointegrating regressions," Journal of Econometrics, Elsevier, vol. 80(2), pages 297-318, October.
  32. Boswijk, Peter & Franses, Philip Hans, 1992. "Dynamic Specification and Cointegration," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 369-81, August.
  33. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
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:bla:jtsera:v:28:y:2007:i:1:p:111-137. 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: (Wiley-Blackwell Digital Licensing)

or (Christopher F. Baum)

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.