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

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  • Elena Pesavento

Abstract

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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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

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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).
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  7. Pesavento, Elena, 2004. "Analytical evaluation of the power of tests for the absence of cointegration," Journal of Econometrics, Elsevier, vol. 122(2), pages 349-384, October.
  8. Peter C.B. Phillips, 1985. "Understanding Spurious Regressions in Econometrics," Cowles Foundation Discussion Papers 757, Cowles Foundation for Research in Economics, Yale University.
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  25. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
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Cited by:
  1. Wallace, Frederick, 2009. "Cointegration tests of purchasing power parity," MPRA Paper 18079, University Library of Munich, Germany.
  2. Pesavento, Elena, 2004. "Analytical evaluation of the power of tests for the absence of cointegration," Journal of Econometrics, Elsevier, vol. 122(2), pages 349-384, October.
  3. Tsen, Wong Hock, 2011. "The real exchange rate determination: An empirical investigation," International Review of Economics & Finance, Elsevier, vol. 20(4), pages 800-811, October.

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