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Testing for Multiple Structural Changes in Cointegrated Regression Models

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Author Info
Mohitosh Kejriwal
Pierre Perron

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Abstract

This paper considers issues related to testing for multiple structural changes in cointegrated systems. We derive the limiting distribution of the Sup-Wald test under mild conditions on the errors and regressors for a variety of testing problems. We show that even if the coefficients of the integrated regressors are held fixed but the intercept is allowed to change, the limit distributions are not the same as would prevail in a stationary framework. Including stationary regressors whose coefficients are not allowed to change does not affect the limiting distribution of the tests under the null hypothesis. We also propose a procedure that allows one to test the null hypothesis of, say, k changes, versus the alternative hypothesis of k + 1 changes. This sequential procedure is useful in that it permits consistent estimation of the number of breaks present. We show via simulations that our tests maintain the correct size in finite samples and are much more powerful than the commonly used LM tests, which suffer from important problems of non-monotonic power in the presence of serial correlation in the errors.

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Paper provided by Purdue University, Department of Economics in its series Purdue University Economics Working Papers with number 1216.

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Length: 41 pages
Date of creation: Nov 2008
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Handle: RePEc:pur:prukra:1216

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Related research
Keywords: change-point; sequential procedure; wald tests; unit roots; cointegration;

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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Jushan Bai, 1997. "Estimation Of A Change Point In Multiple Regression Models," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 551-563, November. [Downloadable!] (restricted)
  2. Zhongjun Qu, 2007. "Searching for cointegration in a dynamic system," Econometrics Journal, Royal Economic Society, vol. 10(3), pages 580-604, November. [Downloadable!] (restricted)
  3. Zhongjun Qu & Pierre Perron, 2007. "Estimating and Testing Structural Changes in Multivariate Regressions," Econometrica, Econometric Society, vol. 75(2), pages 459-502, 03. [Downloadable!] (restricted)
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  4. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November. [Downloadable!] (restricted)
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  5. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May. [Downloadable!] (restricted)
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  6. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July. [Downloadable!] (restricted)
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  7. Seo, Byeongseon, 1998. "Tests For Structural Change In Cointegrated Systems," Econometric Theory, Cambridge University Press, vol. 14(02), pages 222-259, April. [Downloadable!]
  8. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(01), pages 1-21, March. [Downloadable!]
  9. Hao, K., 1996. "Testing for Structural Change in Cointegrated Regression Models: Some Comparisons and Generalizations," Monash Econometrics and Business Statistics Working Papers 3/96, Monash University, Department of Econometrics and Business Statistics.
  10. Hansen, Peter Reinhard, 2003. "Structural changes in the cointegrated vector autoregressive model," Journal of Econometrics, Elsevier, vol. 114(2), pages 261-295, June. [Downloadable!] (restricted)
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  11. Kang Hao, 1996. "Testing for structural change in cointegrated regression models: some comparisons and generalizations," Econometric Reviews, Taylor and Francis Journals, vol. 15(4), pages 401-429. [Downloadable!] (restricted)
  12. 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. [Downloadable!] (restricted)
  13. Bai, Jushan & Lumsdaine, Robin L & Stock, James H, 1998. "Testing for and Dating Common Breaks in Multivariate Time Series," Review of Economic Studies, Blackwell Publishing, vol. 65(3), pages 395-432, July. [Downloadable!] (restricted)
  14. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22. [Downloadable!]
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  15. Kejriwal, Mohitosh & Perron, Pierre, 2008. "The limit distribution of the estimates in cointegrated regression models with multiple structural changes," Journal of Econometrics, Elsevier, vol. 146(1), pages 59-73, September. [Downloadable!] (restricted)
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  16. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
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  17. Hansen, Bruce E, 1992. "Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes," Econometrica, Econometric Society, vol. 60(4), pages 967-72, July. [Downloadable!] (restricted)
  18. Perron, Pierre & Zhu, Xiaokang, 2005. "Structural breaks with deterministic and stochastic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 65-119. [Downloadable!] (restricted)
  19. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-56, July. [Downloadable!] (restricted)
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Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Jing Zhou & Pierre Perron, 2008. "Testing for Breaks in Coefficients and Error Variance: Simulations and Applications," Boston University - Department of Economics - Working Papers Series wp2008-010, Boston University - Department of Economics. [Downloadable!]
  2. Andreas Beyer & Alfred A. Haug & William G. Dewald, 2009. "Structural Breaks, Cointegration and the Fisher Effect," Working Paper Series 1013, European Central Bank. [Downloadable!]
  3. Boetel, Brenda L. & Liu, Donald J., 2008. "Incorporating Structural Changes in Agricultural and Food Price Analysis: An Application to the U.S. Beef and Pork Sectors," Working Papers 44076, University of Minnesota, The Food Industry Center. [Downloadable!]
  4. Pierre Perron & Jing Zhou, 2008. "Testing Jointly for Structural Changes in the Error Variance and Coefficients of a Linear Regression Model," Boston University - Department of Economics - Working Papers Series wp2008-011, Boston University - Department of Economics. [Downloadable!]
  5. Mohitosh Kejriwal & Pierre Perron, 2006. "The Limit Distribution of the Estimates in Cointegrated Regression Models with Multiple Structural Changes," Boston University - Department of Economics - Working Papers Series WP2006-064, Boston University - Department of Economics. [Downloadable!]
    Other versions:
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