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Testing for Multiple Structural Changes in Cointegrated Regression Models

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  • Mohitosh Kejriwal
  • Pierre Perron

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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Bibliographic Info

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
Date of revision:
Handle: RePEc:pur:prukra:1216

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

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References

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  1. Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 9552, Universite de Montreal, Departement de sciences economiques.
  2. Hansen, Bruce E, 1992. "Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes," Econometrica, Econometric Society, Econometric Society, vol. 60(4), pages 967-72, July.
  3. Perron, Pierre & Zhu, Xiaokang, 2005. "Structural breaks with deterministic and stochastic trends," Journal of Econometrics, Elsevier, Elsevier, vol. 129(1-2), pages 65-119.
  4. Seo, Byeongseon, 1998. "Tests For Structural Change In Cointegrated Systems," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 14(02), pages 222-259, April.
  5. Josep Lluís Carrion-i-Silvestre & Andreu Sansó, 2006. "Testing the Null of Cointegration with Structural Breaks," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, Department of Economics, University of Oxford, vol. 68(5), pages 623-646, October.
  6. Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1015, Cowles Foundation for Research in Economics, Yale University.
  7. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
  8. Kuo, Biing-Shen, 1998. "Test for partial parameter instability in regressions with I(1) processes," Journal of Econometrics, Elsevier, Elsevier, vol. 86(2), pages 337-368, June.
  9. 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, Wiley Blackwell, vol. 65(3), pages 395-432, July.
  10. Hansen, Peter Reinhard, 2003. "Structural changes in the cointegrated vector autoregressive model," Journal of Econometrics, Elsevier, Elsevier, vol. 114(2), pages 261-295, June.
  11. Ng, S. & Perron, P., 1995. "Estimation and Inference in Nearly Unbalanced, Nearly Cointegrated Systems," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 9534, Universite de Montreal, Departement de sciences economiques.
  12. Zhongjun Qu, 2007. "Searching for cointegration in a dynamic system," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 10(3), pages 580-604, November.
  13. Bruce E. Hansen, 1998. "Testing for Structural Change in Conditional Models," Boston College Working Papers in Economics, Boston College Department of Economics 310., Boston College Department of Economics.
  14. Kejriwal, Mohitosh, 2009. "Tests for a mean shift with good size and monotonic power," Economics Letters, Elsevier, Elsevier, vol. 102(2), pages 78-82, February.
  15. Hao, K., 1996. "Testing for Structural Change in Cointegrated Regression Models: Some Comparisons and Generalizations," Monash Econometrics and Business Statistics Working Papers, Monash University, Department of Econometrics and Business Statistics 3/96, Monash University, Department of Econometrics and Business Statistics.
  16. Kejriwal, Mohitosh & Perron, Pierre, 2008. "The limit distribution of the estimates in cointegrated regression models with multiple structural changes," Journal of Econometrics, Elsevier, Elsevier, vol. 146(1), pages 59-73, September.
  17. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, Econometric Society, vol. 59(3), pages 817-58, May.
  18. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, Econometric Society, vol. 61(4), pages 821-56, July.
  19. Zhongjun Qu & Pierre Perron, 2007. "Estimating and Testing Structural Changes in Multivariate Regressions," Econometrica, Econometric Society, Econometric Society, vol. 75(2), pages 459-502, 03.
  20. Jushan Bai, 1997. "Estimation Of A Change Point In Multiple Regression Models," The Review of Economics and Statistics, MIT Press, MIT Press, vol. 79(4), pages 551-563, November.
  21. Hansen, Bruce E., 1992. "Efficient estimation and testing of cointegrating vectors in the presence of deterministic trends," Journal of Econometrics, Elsevier, Elsevier, vol. 53(1-3), pages 87-121.
  22. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 7(01), pages 1-21, March.
  23. Quintos, Carmela E & Phillips, Peter C B, 1993. "Parameter Constancy in Cointegrating Regressions," Empirical Economics, Springer, Springer, vol. 18(4), pages 675-706.
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