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Pitfalls of Two Step Testing for Changes in the Error Variance and Coefficients of a Linear Regression Model

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  • Perron, Pierre
  • Yamamoto, Yohei
  • 山本, 庸平

Abstract

In empirical applications based on linear regression models, structural changes often occur in both the error variance and regression coefficients, possibly at different dates. A commonly applied method is to first test for changes in the coefficients (or in the error variance) and, conditional on the break dates found, test for changes in the variance (or in the coefficients). In this note, we provide evidence that such procedures have poor finite sample properties when the changes in the first step are not correctly accounted for. In doing so, we show that testing for changes in the coefficients (or in the variance) ignoring changes in the variance (or in the coefficients) induces size distortions and loss of power. Our results illustrate a need for a joint approach to test for structural changes in both the coefficients and the variance of the errors. We provide some evidence that the procedures suggested by Perron et al. (2019) provide tests with good size and power.
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Suggested Citation

  • Perron, Pierre & Yamamoto, Yohei & 山本, 庸平, 2019. "Pitfalls of Two Step Testing for Changes in the Error Variance and Coefficients of a Linear Regression Model," Discussion Papers 2019-01, Graduate School of Economics, Hitotsubashi University.
    • Handle: RePEc:hit:econdp:2019-01
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    References listed on IDEAS

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    1. Deng, Ai & Perron, Pierre, 2008. "A non-local perspective on the power properties of the CUSUM and CUSUM of squares tests for structural change," Journal of Econometrics, Elsevier, vol. 142(1), pages 212-240, January.
    2. 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.
    3. 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.
    4. 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.
    5. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    6. Zhongjun Qu & Pierre Perron, 2007. "Estimating and Testing Structural Changes in Multivariate Regressions," Econometrica, Econometric Society, vol. 75(2), pages 459-502, March.
    7. 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.
    8. 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.
    9. Herrera, Ana Maria & Pesavento, Elena, 2005. "The Decline in U.S. Output Volatility: Structural Changes and Inventory Investment," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 462-472, October.
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    Cited by:

    1. 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.
    2. Daiki Maki & Yasushi Ota, 2021. "Testing for Time-Varying Properties Under Misspecified Conditional Mean and Variance," Computational Economics, Springer;Society for Computational Economics, vol. 57(4), pages 1167-1182, April.
    3. 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.
    4. Daiki Maki & Yasushi Ota, 2019. "Testing for time-varying properties under misspecified conditional mean and variance," Papers 1907.12107, arXiv.org, revised Aug 2019.
    5. 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.
    6. Ashok Chanabasangouda Patil & Shailesh Rastogi, 2020. "Multifractal Analysis of Market Efficiency across Structural Breaks: Implications for the Adaptive Market Hypothesis," JRFM, MDPI, vol. 13(10), pages 1-18, October.

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    More about this item

    Keywords

    structural change; variance shifts; CUSUM of squares tests; hypothesis testing; Sup-LR test;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis

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