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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. Our asymptotic results show that as long as the intercept is allowed to change across regimes, inference is possible even if we allow stationary variables in the regression. We also find that including stationary regressors whose coefficients are not allowed to change does not affect the limiting distribution of the tests under the null hypothesis. We propose a procedure that allows one to test the null hypothesis of, say, changes, versus the alternative hypothesis of changes. This sequential procedure is useful in that it permits consistent estimation of the number of breaks present. When the regression is spurious, we show that the procedure tends to select the maximum number of breaks allowed. This feature helps distinguish a cointegrated model from a purely spurious one. Our simulation experiments show that in the presence of serial correlation in the errors, the commonly used LM tests suffer from the important problem of nonmonotonic power in finite samples. In fact, in certain cases, power can go to zero as the magnitude of the break(s) increase. We propose a modified Wald test based on a new estimator of the long run variance which uses information under both the null and alternative hypotheses. The proposed test is able to mitigate size distortions associated with the usual Wald test while maintaining monotonic power.

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Bibliographic Info

Paper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number WP2006-051.

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Length: 63 pages
Date of creation: Sep 2006
Date of revision:
Handle: RePEc:bos:wpaper:wp2006-051

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Keywords: Change-point; Sequential procedure; Wald tests; Unit Roots; Cointegration.;

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References

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  1. Hansen, Bruce E, 1992. "Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes," Econometrica, Econometric Society, Econometric Society, vol. 60(4), pages 967-72, July.
  2. 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.
  3. Hansen, Peter Reinhard, 2003. "Structural changes in the cointegrated vector autoregressive model," Journal of Econometrics, Elsevier, Elsevier, vol. 114(2), pages 261-295, June.
  4. Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation for Research in Economics, Yale University.
  5. 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.
  6. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, Elsevier, vol. 97(1), pages 93-115, July.
  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. Perron, Pierre & Zhu, Xiaokang, 2005. "Structural breaks with deterministic and stochastic trends," Journal of Econometrics, Elsevier, Elsevier, vol. 129(1-2), pages 65-119.
  9. Zhongjun Qu & Pierre Perron, 2005. "Estimating and testing structural changes in multivariate regressions," Boston University - Department of Economics - Working Papers Series, Boston University - Department of Economics WP2005-012, Boston University - Department of Economics.
  10. Ng, Serena & Perron, Pierre, 1997. "Estimation and inference in nearly unbalanced nearly cointegrated systems," Journal of Econometrics, Elsevier, Elsevier, vol. 79(1), pages 53-81, July.
  11. Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche, Centre interuniversitaire de recherche en économie quantitative, CIREQ 9552, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  12. Zhongjun Qu, 2007. "Searching for cointegration in a dynamic system," Econometrics Journal, Royal Economic Society, vol. 10(3), pages 580-604, November.
  13. 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.
  14. Kejriwal, Mohitosh, 2009. "Tests for a mean shift with good size and monotonic power," Economics Letters, Elsevier, vol. 102(2), pages 78-82, February.
  15. 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.
  16. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(01), pages 1-21, March.
  17. 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, Boston University - Department of Economics WP2006-064, Boston University - Department of Economics.
  18. 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, vol. 68(5), pages 623-646, October.
  19. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, Econometric Society, vol. 59(3), pages 817-58, May.
  20. Quintos, Carmela E & Phillips, Peter C B, 1993. "Parameter Constancy in Cointegrating Regressions," Empirical Economics, Springer, vol. 18(4), pages 675-706.
  21. 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.
  22. Seo, Byeongseon, 1998. "Tests For Structural Change In Cointegrated Systems," Econometric Theory, Cambridge University Press, vol. 14(02), pages 222-259, April.
  23. 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.
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