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

Author

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  • 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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    Cited by:

    1. 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.
    2. Pierre Perron & Yohei Yamamoto, 2019. "Pitfalls of Two-Step Testing for Changes in the Error Variance and Coefficients of a Linear Regression Model," Econometrics, MDPI, vol. 7(2), pages 1-11, May.
    3. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    4. 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.
    5. Esteve Vicente & Prats Maria A., 2021. "Structural Breaks and Explosive Behavior in the Long-Run: The Case of Australian Real House Prices, 1870–2020," Economics - The Open-Access, Open-Assessment Journal, De Gruyter, vol. 15(1), pages 72-84, January.
    6. Kostyrka, Andreï & Malakhov, Dmitry, 2021. "Was there ever a shift: Empirical analysis of structural-shift tests for return volatility," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 61, pages 110-139.
    7. Bai, Jushan & Duan, Jiangtao & Han, Xu, 2024. "The likelihood ratio test for structural changes in factor models," Journal of Econometrics, Elsevier, vol. 238(2).
    8. Emilio Congregado & Carmen Díaz-Roldán & Vicente Esteve, 2023. "Deficit sustainability and fiscal theory of price level: the case of Italy, 1861–2020," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 50(3), pages 755-782, August.
    9. Mohitosh Kejriwal & Xuewen Yu & Pierre Perron, 2020. "Bootstrap procedures for detecting multiple persistence shifts in heteroskedastic time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(5), pages 676-690, September.
    10. 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.
    11. Yohei Yamamoto & Naoko Hara, 2022. "Identifying factor‐augmented vector autoregression models via changes in shock variances," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(4), pages 722-745, June.
    12. 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.
    13. Manner, Hans & Rodríguez, Gabriel & Stöckler, Florian, 2024. "A changepoint analysis of exchange rate and commodity price risks for Latin American stock markets," International Review of Economics & Finance, Elsevier, vol. 89(PA), pages 1385-1403.
    14. Pierre Perron & Yohei Yamamoto, 2022. "The great moderation: updated evidence with joint tests for multiple structural changes in variance and persistence," Empirical Economics, Springer, vol. 62(3), pages 1193-1218, March.
    15. Vicente Esteve & María A. Prats, 2021. "Testing for rational bubbles in Australian housing market from a long-term perspective," Working Papers 2113, Department of Applied Economics II, Universidad de Valencia.
    16. 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.
    17. De Lipsis Vincenzo, 2021. "Dating Structural Changes in UK Monetary Policy," The B.E. Journal of Macroeconomics, De Gruyter, vol. 21(2), pages 509-539, June.
    18. Wu, Jilin, 2016. "Detecting structural changes under nonstationary volatility," Economics Letters, Elsevier, vol. 146(C), pages 151-154.
    19. Shahnaz Parsaeian, 2024. "Stein-like Common Correlated Effects Estimation under Structural Breaks," Econometrics, MDPI, vol. 12(2), pages 1-23, April.
    20. Yang, Yao & Karali, Berna, 2022. "How far is too far for volatility transmission?," Journal of Commodity Markets, Elsevier, vol. 26(C).
    21. Congregado, Emilio & Esteve, Vicente, 2022. "Cointegration with structural changes and classical model of inflation in Spain, 1830–1998," Structural Change and Economic Dynamics, Elsevier, vol. 60(C), pages 376-388.

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    More about this item

    Keywords

    Change-point; Variance shift; Conditional heteroskedasticity; Likelihood ratio tests;
    All these keywords.

    JEL classification:

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

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