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Analytical Evaluation of the Power of Tests for the Absence of Cointegration

  • PESAVENTO, ELENA

This paper proposes a theoretical explanation to the common empirical results in which different tests for cointegration give different answers. Using local to unity parametrization I compute the analytical power of some tests for the null of no cointegration: The ADF test on the residuals of the cointegration regression, Johansen's maximum eigenvalue test, the t-test on the Error Correction term and Boswijk (1994) Wald test. The tests are shown to be functions of Brownian Motions and Ornstein-Uhlenbeck processes and to depend on a single nuisance parameter, which is, in turn determined by the correlation at frequency zero of the independent variables with the errors of the cointegration regression. Monte Carlo experiments show that the tests can have significantly different performances for different values of the nuisance parameter. An application to the money demand equation is presented.

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Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number qt4cq4773c.

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Date of creation: 01 Sep 2000
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Handle: RePEc:cdl:ucsdec:qt4cq4773c
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  1. Haug, Alfred A., 1996. "Tests for cointegration a Monte Carlo comparison," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 89-115.
  2. Harbo, Ingrid, et al, 1998. "Asymptotic Inference on Cointegrating Rank in Partial Systems," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(4), pages 388-99, October.
  3. Jeroen J.M. Kremers & Neil R. Ericsson & Juan J. Dolado, 1992. "The power of cointegration tests," International Finance Discussion Papers 431, Board of Governors of the Federal Reserve System (U.S.).
  4. Zhijie Xiao & Peter C.B. Phillips, 1997. "An ADF Coefficient Test for a Unit Root in ARMA Models of Unknown Order with Empirical Applications to the U.S. Economy," Cowles Foundation Discussion Papers 1161, Cowles Foundation for Research in Economics, Yale University.
  5. Jansson, Michael & Haldrup, Niels, 2002. "Regression Theory For Nearly Cointegrated Time Series," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1309-1335, December.
  6. Saikkonen, Pentti & Lütkepohl, Helmut, 1997. "Local power of likelihood ratio tests for the cointegrating rank of a VAR process," SFB 373 Discussion Papers 1997,58, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  7. Neil R. Ericsson & James G. MacKinnon, 2000. "Distributions of Error Correction Tests for Cointegration," Econometric Society World Congress 2000 Contributed Papers 0561, Econometric Society.
  8. Phillips, Peter C B, 1988. "Regression Theory for Near-Integrated Time Series," Econometrica, Econometric Society, vol. 56(5), pages 1021-43, September.
  9. 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.
  10. 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.
  11. 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.
  12. Saikkonen, Pentti & Lütkepohl, Helmut, 1998. "Testing for the cointegrating rank of a VAR process with an intercept," SFB 373 Discussion Papers 1998,51, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  13. Gonzalo, J. & Lee, T.H., 1995. "Pitfalls in Testing for Long Run Relationships," Papers 38, Boston University - Department of Economics.
  14. Saikkonen, Pentti, 1992. "Estimation and Testing of Cointegrated Systems by an Autoregressive Approximation," Econometric Theory, Cambridge University Press, vol. 8(01), pages 1-27, March.
  15. Lutkepohl, Helmut & Saikkonen, Pentti, 2000. "Testing for the cointegrating rank of a VAR process with a time trend," Journal of Econometrics, Elsevier, vol. 95(1), pages 177-198, March.
  16. Johansen, Soren & Juselius, Katarina, 1990. "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 52(2), pages 169-210, May.
  17. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
  18. Bewley, R. & Yang, M., 1996. "On the Size and Power of System Tests for Cointegration," Papers 96/9, New South Wales - School of Economics.
  19. 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.
  20. Horvath, Michael T.K. & Watson, Mark W., 1995. "Testing for Cointegration When Some of the Cointegrating Vectors are Prespecified," Econometric Theory, Cambridge University Press, vol. 11(05), pages 984-1014, October.
  21. 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.
  22. Jeremy Berkowitz & Lutz Kilian, 2000. "Recent developments in bootstrapping time series," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 1-48.
  23. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
  24. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(01), pages 1-21, March.
  25. Graham Elliott, 1998. "On the Robustness of Cointegration Methods when Regressors Almost Have Unit Roots," Econometrica, Econometric Society, vol. 66(1), pages 149-158, January.
  26. Li, Hongyi & Maddala, G. S., 1997. "Bootstrapping cointegrating regressions," Journal of Econometrics, Elsevier, vol. 80(2), pages 297-318, October.
  27. 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.
  28. Phillips, Peter C B & Hansen, Bruce E, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Wiley Blackwell, vol. 57(1), pages 99-125, January.
  29. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
  30. Atsushi Inoue & Lutz Kilian, 2000. "Bootstrapping Autoregressive Processes with Possible Unit Roots," Econometric Society World Congress 2000 Contributed Papers 0401, Econometric Society.
  31. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  32. Zivot, Eric, 2000. "The Power Of Single Equation Tests For Cointegration When The Cointegrating Vector Is Prespecified," Econometric Theory, Cambridge University Press, vol. 16(03), pages 407-439, June.
  33. Elena Pesavento, 2005. "Residuals Based Tests for the Null of No Cointegration: An Analytical Comparison," Emory Economics 0503, Department of Economics, Emory University (Atlanta).
  34. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-44, January.
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