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

  • Pierre Perron

    ()

    (Boston University)

  • Jing Zhou

    ()

    (BlackRock, Inc.)

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.

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Paper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number wp2008-011.

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Length: 35
Date of creation: Jul 2008
Date of revision:
Handle: RePEc:bos:wpaper:wp2008-011
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Web page: http://www.bu.edu/econ/

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  1. Bai, Jushan, 1999. "Likelihood ratio tests for multiple structural changes," Journal of Econometrics, Elsevier, vol. 91(2), pages 299-323, August.
  2. Mohitosh Kejriwal & Pierre Perron, 2006. "Testing for Multiple Structural Changes in Cointegrated Regression Models," Boston University - Department of Economics - Working Papers Series WP2006-051, Boston University - Department of Economics.
  3. 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.
  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. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  6. 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.
  7. 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.
  8. 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.
  9. Donald W.K. Andrews, 1990. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Cowles Foundation Discussion Papers 943, Cowles Foundation for Research in Economics, Yale University.
  10. Kejriwal, Mohitosh, 2009. "Tests for a mean shift with good size and monotonic power," Economics Letters, Elsevier, vol. 102(2), pages 78-82, February.
  11. 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.
  12. 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, vol. 65(3), pages 395-432, July.
  13. Perron, Pierre & Qu, Zhongjun, 2006. "Estimating restricted structural change models," Journal of Econometrics, Elsevier, vol. 134(2), pages 373-399, October.
  14. Bruce E. Hansen, 1998. "Testing for Structural Change in Conditional Models," Boston College Working Papers in Economics 310., Boston College Department of Economics.
  15. 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, 06.
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