IDEAS home Printed from https://ideas.repec.org/a/bes/jnlbes/v28i4y2010p503-522.html
   My bibliography  Save this article

Testing for Multiple Structural Changes in Cointegrated Regression Models

Author

Listed:
  • Kejriwal, Mohitosh
  • Perron, Pierre

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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Kejriwal, Mohitosh & Perron, Pierre, 2010. "Testing for Multiple Structural Changes in Cointegrated Regression Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 503-522.
  • Handle: RePEc:bes:jnlbes:v:28:i:4:y:2010:p:503-522
    as

    Download full text from publisher

    File URL: http://pubs.amstat.org/doi/abs/10.1198/jbes.2009.07220
    File Function: full text
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    2. Zhongjun Qu, 2007. "Searching for cointegration in a dynamic system," Econometrics Journal, Royal Economic Society, vol. 10(3), pages 580-604, November.
    3. Kejriwal, Mohitosh & Perron, Pierre, 2008. "Data Dependent Rules For Selection Of The Number Of Leads And Lags In The Dynamic Ols Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1425-1441, October.
    4. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    5. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    6. Seo, Byeongseon, 1998. "Tests For Structural Change In Cointegrated Systems," Econometric Theory, Cambridge University Press, vol. 14(2), pages 222-259, April.
    7. 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.
    8. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    9. 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.
    10. 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.
    11. Hansen, Bruce E, 1992. "Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes," Econometrica, Econometric Society, vol. 60(4), pages 967-972, July.
    12. Perron, Pierre & Zhu, Xiaokang, 2005. "Structural breaks with deterministic and stochastic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 65-119.
    13. Hansen, Peter Reinhard, 2003. "Structural changes in the cointegrated vector autoregressive model," Journal of Econometrics, Elsevier, vol. 114(2), pages 261-295, June.
    14. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    15. Quintos, Carmela E & Phillips, Peter C B, 1993. "Parameter Constancy in Cointegrating Regressions," Empirical Economics, Springer, vol. 18(4), pages 675-706.
    16. Corbae,Dean & Durlauf,Steven N. & Hansen,Bruce E. (ed.), 2006. "Econometric Theory and Practice," Cambridge Books, Cambridge University Press, number 9780521807234, October.
    17. 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.
    18. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    19. Kuo, Biing-Shen, 1998. "Test for partial parameter instability in regressions with I(1) processes," Journal of Econometrics, Elsevier, vol. 86(2), pages 337-368, June.
    20. Zhongjun Qu & Pierre Perron, 2007. "Estimating and Testing Structural Changes in Multivariate Regressions," Econometrica, Econometric Society, vol. 75(2), pages 459-502, March.
    21. Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, vol. 61(4), pages 783-820, July.
    22. Ng, Serena & Perron, Pierre, 1997. "Estimation and inference in nearly unbalanced nearly cointegrated systems," Journal of Econometrics, Elsevier, vol. 79(1), pages 53-81, July.
    23. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(1), pages 1-21, March.
    24. 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.
    25. 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.
    26. 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.
    27. Kejriwal, Mohitosh, 2009. "Tests for a mean shift with good size and monotonic power," Economics Letters, Elsevier, vol. 102(2), pages 78-82, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Boston University - Department of Economics - Working Papers Series WP2019-02, Boston University - Department of Economics.
    3. Skrobotov, Anton, 2021. "Structural breaks in cointegration models," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 63, pages 117-141.
    4. Karsten Schweikert, 2020. "Oracle Efficient Estimation of Structural Breaks in Cointegrating Regressions," Papers 2001.07949, arXiv.org, revised Apr 2021.
    5. Oka, Tatsushi & Perron, Pierre, 2018. "Testing for common breaks in a multiple equations system," Journal of Econometrics, Elsevier, vol. 204(1), pages 66-85.
    6. Matteo Mogliani, 2010. "Residual-based tests for cointegration and multiple deterministic structural breaks: A Monte Carlo study," Working Papers halshs-00564897, HAL.
    7. Ye Li & Pierre Perron, 2017. "Inference on locally ordered breaks in multiple regressions," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 289-353, March.
    8. Eiji Kurozumi & Anton Skrobotov, 2018. "Confidence Sets for the Break Date in Cointegrating Regressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 80(3), pages 514-535, June.
    9. Karsten Schweikert, 2022. "Oracle Efficient Estimation of Structural Breaks in Cointegrating Regressions," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(1), pages 83-104, January.
    10. Pierre Perron & Yohei Yamamoto & Jing Zhou, 2020. "Testing jointly for structural changes in the error variance and coefficients of a linear regression model," Quantitative Economics, Econometric Society, vol. 11(3), pages 1019-1057, July.
    11. Eiji Kurozumi & Yoichi Arai, 2007. "Efficient estimation and inference in cointegrating regressions with structural change," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(4), pages 545-575, July.
    12. Pierre Perron & Yohei Yamamoto, 2022. "Structural change tests under heteroskedasticity: Joint estimation versus two‐steps methods," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 389-411, May.
    13. Seong Yeon Chang & Pierre Perron, 2016. "Inference on a Structural Break in Trend with Fractionally Integrated Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(4), pages 555-574, July.
    14. Esteve, Vicente & Navarro-Ibáñez, Manuel & Prats, María A., 2013. "The Spanish term structure of interest rates revisited: Cointegration with multiple structural breaks, 1974–2010," International Review of Economics & Finance, Elsevier, vol. 25(C), pages 24-34.
    15. Alaa Abi Morshed & Elena Andreou & Otilia Boldea, 2018. "Structural Break Tests Robust to Regression Misspecification," Econometrics, MDPI, vol. 6(2), pages 1-39, May.
    16. Mohitosh Kejriwal & Pierre Perron & Xuewen Yu, 2022. "A two‐step procedure for testing partial parameter stability in cointegrated regression models," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(2), pages 219-237, March.
    17. Beyer, Andreas & Dewald, William G. & Haug, Alfred A., 2009. "Structural breaks, cointegration and the Fisher effect," Working Paper Series 1013, European Central Bank.
    18. Narayan, Seema & Smyth, Russell, 2015. "The financial econometrics of price discovery and predictability," International Review of Financial Analysis, Elsevier, vol. 42(C), pages 380-393.
    19. Kuo, Biing-Shen, 1998. "Test for partial parameter instability in regressions with I(1) processes," Journal of Econometrics, Elsevier, vol. 86(2), pages 337-368, June.
    20. Rossi, Barbara, 2013. "Advances in Forecasting under Instability," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1203-1324, Elsevier.

    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bes:jnlbes:v:28:i:4:y:2010:p:503-522. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://www.amstat.org/publications/jbes/index.cfm?fuseaction=main .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Christopher F. Baum (email available below). General contact details of provider: http://www.amstat.org/publications/jbes/index.cfm?fuseaction=main .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.