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Testing for the Null Hypothesis of Cointegration with Structural Breaks (Subsequently published in "Econometric Reviews", Volume 26, Issue 6 November 2007, pages 705 - 739. )

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  • Yoichi Arai

    (Faculty of Economics, University of Tokyo)

  • Eiji Kurozumi

    (Department of Economics, Hitotsubashi University)

Abstract

In this paper we propose residual-based tests for the null hypothesis of cointegration with structural breaks against the alternative of no cointegration. The Lagrange Multiplier test is proposed and its limiting distribution is obtained for the case in which the timing of a structural break is known. Then the test statistic is extended in two ways to deal with a structural break of unknown timing. The first test statistic, a plug-in version of the test statistic for known timing, replaces the true break point by the estimated one. We also propose a second test statistic where the break point is chosen to be most favorable for the null hypothesis. We show the limiting properties of both statistics under the null as well as the alternative. Critical values are calculated for the tests by simulation methods. Finite-sample simulations show that the empirical size of the test is close to the nominal one unless the regression error is very persistent and that the test rejects the null when no cointegrating relationship with a structural break is present.

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Bibliographic Info

Paper provided by Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo in its series CARF F-Series with number CARF-F-022.

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Length: 41 pages
Date of creation: Feb 2005
Date of revision:
Handle: RePEc:cfi:fseres:cf022

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  1. Kurozumi, Eiji & Arai, Yoichi, 2005. "Efficient Estimation and Inference in Cointegrating Regressions with Structural Change," Discussion Papers 2004-09, Graduate School of Economics, Hitotsubashi University.
  2. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(01), pages 1-21, March.
  3. Inoue, Atsushi, 1999. "Tests of cointegrating rank with a trend-break," Journal of Econometrics, Elsevier, vol. 90(2), pages 215-237, June.
  4. Helmut Luetkepohl & Pentti Saikkonen & Carsten Trenkler, 2000. "Comparison of Tests for the Cointegrating Rank of a VAR Process with a Structural Shift," Econometric Society World Congress 2000 Contributed Papers 0364, Econometric Society.
  5. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
  6. 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.
  7. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  8. Yoichi Arai, 2004. "Testing for Linearity in Regressions with I (1) processes," CARF F-Series CARF-F-014, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  9. Shin, Yongcheol, 1994. "A Residual-Based Test of the Null of Cointegration Against the Alternative of No Cointegration," Econometric Theory, Cambridge University Press, vol. 10(01), pages 91-115, March.
  10. Peter C.B. Phillips & Steven N. Durlauf, 1985. "Multiple Time Series Regression with Integrated Processes," Cowles Foundation Discussion Papers 768, Cowles Foundation for Research in Economics, Yale University.
  11. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  12. Bai, Jushan & Lumsdaine, Robin L & Stock, James H, 1998. "Testing for and Dating Common Breaks in Multivariate Time Series," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 395-432, July.
  13. Peter Reinhard Hansen, 2000. "Structural Changes in the Cointegrated Vector Autoregressive Model," Working Papers 2000-20, Brown University, Department of Economics.
  14. Helmut Lütkepohl & Pentti Saikkonen & Carsten Trenkler, 2004. "Testing for the Cointegrating Rank of a VAR Process with Level Shift at Unknown Time," Econometrica, Econometric Society, vol. 72(2), pages 647-662, 03.
  15. G. William Schwert, 1988. "Tests For Unit Roots: A Monte Carlo Investigation," NBER Technical Working Papers 0073, National Bureau of Economic Research, Inc.
  16. 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.
  17. 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.
  18. Saikkonen, Pentti & Lütkepohl, Helmut, 2001. "Testing for the cointegrating rank of a VAR process with structural shifts," SFB 373 Discussion Papers 1998,82, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  19. Allan w. Gregory & Bruce E. Hansen, 1992. "residual-Based Tests for Cointegration in Models with Regime Shifts," Working Papers 862, Queen's University, Department of Economics.
  20. Kurozumi, Eiji, 2002. "Testing for stationarity with a break," Journal of Econometrics, Elsevier, vol. 108(1), pages 63-99, May.
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