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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. )

  • Yoichi Arai

    (Faculty of Economics, University of Tokyo)

  • Eiji Kurozumi

    (Department of Economics, Hitotsubashi University)

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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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. Eric Zivot & Donald W.K. Andrews, 1990. "Further Evidence on the Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Cowles Foundation Discussion Papers 944, Cowles Foundation for Research in Economics, Yale University.
  2. 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.
  3. 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.
  4. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
  5. 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.
  6. Jushan Bai & Robin L. Lumsdaine & James H. Stock, 1998. "Testing For and Dating Common Breaks in Multivariate Time Series," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 395-432.
  7. Yoichi Arai, 2015. "Testing for Linearity in Regressions with I(1) Processes," GRIPS Discussion Papers 15-11, National Graduate Institute for Policy Studies.
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  12. Lütkepohl, Helmut & Saikkonen, Pentti & Trenkler, Carsten, 2000. "Comparison of tests for the cointegrating rank of a VAR process with a structural shift," SFB 373 Discussion Papers 2000,10, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  13. Gregory, A.W. & Hansen, B.E., 1992. "Residual-Based Tests for Cointegration in Models with Regime Shifts," RCER Working Papers 335, University of Rochester - Center for Economic Research (RCER).
  14. 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.
  15. Kurozumi, Eiji, 2002. "Testing for stationarity with a break," Journal of Econometrics, Elsevier, vol. 108(1), pages 63-99, May.
  16. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  17. 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.
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