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Testing Jointly for Structural Changes in the Error Variance and Coefficients of a Linear Regression Model

Author

Listed:
  • Pierre Perron

    () (Boston University)

  • Jing Zhou

    () (BlackRock, Inc.)

Abstract

We provide a comprehensive treatment of the problem of testing jointly for structural change in both the regression coefficients and the variance of the errors in a single equation regression involving stationary regressors. Our framework is quite general in that we allow for general mixing-type regressors and the assumptions imposed on the errors are quite mild. The errors’ distribution can be non-normal and conditional heteroskedasticity is permissable. Extensions to the case with serially correlated errors are also treated. We provide the required tools for addressing the following testing problems, among others: a) testing for given numbers of changes in regression coefficients and variance of the errors; b) testing for some unknown number of changes less than some pre-specified maximum; c) testing for changes in variance (regression coefficients) allowing for a given number of changes in regression coefficients (variance); and d) estimating the number of changes present. These testing problems are important for practical applications as witnessed by recent interests in macroeconomics and finance for which documenting structural change in the variability of shocks to simple autoregressions or vector autoregressive models has been a concern.

Suggested Citation

  • 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.
  • Handle: RePEc:bos:wpaper:wp2008-011
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    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. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    3. 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.
    4. Jean-Yves Pitarakis, 2004. "Least squares estimation and tests of breaks in mean and variance under misspecification," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 32-54, June.
    5. Perron, Pierre & Qu, Zhongjun, 2006. "Estimating restricted structural change models," Journal of Econometrics, Elsevier, vol. 134(2), pages 373-399, October.
    6. Pierre Perron & Yohei Yamamoto, 2008. "Estimating and Testing Multiple Structural Changes in Models with Endogenous Regressors," Boston University - Department of Economics - Working Papers Series wp2008-017, Boston University - Department of Economics.
    7. Jushan Bai, 2000. "Vector Autoregressive Models with Structural Changes in Regression Coefficients and in Variance-Covariance Matrices," Annals of Economics and Finance, Society for AEF, vol. 1(2), pages 303-339, November.
    8. Deng, Ai & Perron, Pierre, 2008. "The Limit Distribution Of The Cusum Of Squares Test Under General Mixing Conditions," Econometric Theory, Cambridge University Press, vol. 24(03), pages 809-822, June.
    9. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    10. 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.
    11. 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.
    12. Bai, Jushan, 1999. "Likelihood ratio tests for multiple structural changes," Journal of Econometrics, Elsevier, vol. 91(2), pages 299-323, August.
    13. 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.
    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. James H. Stock & Mark W. Watson, 2003. "Has the Business Cycle Changed and Why?," NBER Chapters,in: NBER Macroeconomics Annual 2002, Volume 17, pages 159-230 National Bureau of Economic Research, Inc.
    16. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
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    Cited by:

    1. Wu, Jilin, 2016. "Detecting structural changes under nonstationary volatility," Economics Letters, Elsevier, vol. 146(C), pages 151-154.
    2. 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.
    3. repec:wsi:serxxx:v:62:y:2017:i:02:n:s0217590815500496 is not listed on IDEAS
    4. Loredana Ureche-Rangau & Franck Speeg, 2011. "A simple method for variance shift detection at unknown time points," Economics Bulletin, AccessEcon, vol. 31(3), pages 2204-2218.
    5. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    6. Soo-Bin Jeong & Bong-Hwan Kim & Tae-Hwan Kim & Hyung-Ho Moon, 2017. "Unit Root Tests In The Presence Of Multiple Breaks In Variance," The Singapore Economic Review (SER), World Scientific Publishing Co. Pte. Ltd., vol. 62(02), pages 345-361, June.
    7. Zeileis, Achim & Shah, Ajay & Patnaik, Ila, 2010. "Testing, monitoring, and dating structural changes in exchange rate regimes," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1696-1706, June.

    More about this item

    Keywords

    Change-point; Variance shift; Conditional heteroskedasticity; Likelihood ratio tests;

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