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Residuals Based Tests for the Null of No Cointegration: An Analytical Comparison

  • Elena Pesavento

This paper computes 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 OLS and 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 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 different unit root tests 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.

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File URL: http://economics.emory.edu/home/assets/workingpapers/pesavento_05_03_paper.pdf
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Paper provided by Department of Economics, Emory University (Atlanta) in its series Emory Economics with number 0503.

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Date of creation: Jan 2005
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Handle: RePEc:emo:wp2003:0503
Contact details of provider: Web page: http://economics.emory.edu/home/journals/
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  1. Graham Elliott & Michael Jansson & Elena Pesavento, 2003. "Optimal Power For Testing Potential Cointegrating Vectors with Known Parameters for Nonstationarity," Emory Economics 0303, Department of Economics, Emory University (Atlanta).
  2. 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.
  3. Hansen, Bruce E., 1995. "Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power," Econometric Theory, Cambridge University Press, vol. 11(05), pages 1148-1171, October.
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  7. Chang, Yoosoon & Park, Joon & Song, Kevin, 2002. "Bootstrapping Cointegrating Regressions," Working Papers 2002-04, Rice University, Department of Economics.
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  12. 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.
  13. Peter C.B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Cowles Foundation Discussion Papers 1189, Cowles Foundation for Research in Economics, Yale University.
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  15. Bewley, R. & Yang, M., 1996. "On the Size and Power of System Tests for Cointegration," Papers 96/9, New South Wales - School of Economics.
  16. 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.
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  18. Peter C.B. Phillips & Sam Ouliaris, 1987. "Asymptotic Properties of Residual Based Tests for Cointegration," Cowles Foundation Discussion Papers 847R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1988.
  19. 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.
  20. Gonzalo, J. & Lee, T.H., 1995. "Pitfalls in Testing for Long Run Relationships," Papers 38, Boston University - Department of Economics.
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  22. Peter C.B. Phillips, 1986. "Regression Theory for Near-Integrated Time Series," Cowles Foundation Discussion Papers 781R, Cowles Foundation for Research in Economics, Yale University, revised Jan 1987.
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  24. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(03), pages 468-497, December.
  25. Li, Hongyi & Maddala, G. S., 1997. "Bootstrapping cointegrating regressions," Journal of Econometrics, Elsevier, vol. 80(2), pages 297-318, October.
  26. 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.
  27. 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.
  28. Haug, A.A., 1992. "Tests for Cointegration: A Monte Carlo Comparison," Papers 93-2, York (Canada) - Department of Economics.
  29. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
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