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Testing jointly for structural changes in the error variance and coe¢ cients of a linear regression model

Author

Listed:
  • Pierre Perron

    (Boston University)

  • Yohei Yamamoto

    (Hitotsubashi University)

  • Jing Zhou

    (Seeking Sense Investment Management Co., Ltd)

Abstract

We provide a comprehensive treatment for the problem of testing jointly for structural changes in both the regression coe¢ cients and the variance of the errors in a single equation system involving stationary regressors. Our framework is quite general in that we allow for general mixing-type regressors and the assumptions on the errors are quite mild. Their distribution can be non-normal and conditional heteroskedasticity is permitted. Extensions to the case with serially correlated errors are also treated. We provide the required tools to address the following testing problems, among others: a) testing for given numbers of changes in regression coe¢ cients and variance of the errors; b) testing for some unknown number of changes within some pre-specified maximum; c) testing for changes in variance (regression coe¢ cients) allowing for a given number of changes in the regression coe¢ cients (variance); d) a sequential procedure to estimate the number of changes present. These testing problems are important for practical applications as witnessed by interests in macroeconomics and finance where documenting structural changes in the variability of shocks to simple autoregressions or Vector Autoregressive Models has been a concern.

Suggested Citation

  • Pierre Perron & Yohei Yamamoto & Jing Zhou, 2019. "Testing jointly for structural changes in the error variance and coe¢ cients of a linear regression model," Boston University - Department of Economics - Working Papers Series WP2020-010, Boston University - Department of Economics, revised Feb 2020.
    • Handle: RePEc:bos:wpaper:wp2020-010
    as

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    File URL: http://www.bu.edu/econ/files/2020/05/Variance-change-PYZ.pdf
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    References listed on IDEAS

    as
    1. 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(3), pages 809-822, June.
    2. Jushan Bai & Serena Ng, 2005. "Tests for Skewness, Kurtosis, and Normality for Time Series Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 49-60, January.
    3. Zhongjun Qu & Pierre Perron, 2007. "Estimating and Testing Structural Changes in Multivariate Regressions," Econometrica, Econometric Society, vol. 75(2), pages 459-502, March.
    4. 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.
    5. 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)

    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Bai, Jushan & Duan, Jiangtao & Han, Xu, 2024. "The likelihood ratio test for structural changes in factor models," Journal of Econometrics, Elsevier, vol. 238(2).
    6. 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.
    7. 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.
    8. Alessandra Canepa, & Karanasos, Menelaos & Paraskevopoulos, Athanasios & Chini, Emilio Zanetti, 2022. "Forecasting Ination: A GARCH-in-Mean-Level Model with Time Varying Predictability," Department of Economics and Statistics Cognetti de Martiis. Working Papers 202212, University of Turin.
    9. 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.
    10. 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.
    11. 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.
    12. Yang, Yao & Karali, Berna, 2022. "How far is too far for volatility transmission?," Journal of Commodity Markets, Elsevier, vol. 26(C).
    13. Emilio Congregado & Silviano Carmen Díaz-Roldán & Vicente Esteve, 2023. "Deficit sustainability and the Fiscal Theory of the Price Level: the case of Italy, 1861-2020," Working Papers 2301, Department of Applied Economics II, Universidad de Valencia.
    14. 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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