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Power Properties of the Modified CUSUM Tests

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  • JIANG, Peiyun
  • 蒋, 佩芸
  • KUROZUMI, Eiji
  • 黒住, 英司

Abstract

The CUSUM test has played an important role in theory and applications related to structural change, but its drawback is that it loses power when the break is orthogonal to the mean of the regressors. In this study, we consider two modified CUSUM tests that have been proposed, implicitly or explicitly, in the literature to detect such structural changes and investigate the limiting power properties of these tests under a fixed alternative. We demonstrate that the modified tests are superior to the classic tests in terms of both asymptotic theory and in finite samples when detecting an orthogonal structural shift.
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  • JIANG, Peiyun & 蒋, 佩芸 & KUROZUMI, Eiji & 黒住, 英司, 2017. "Power Properties of the Modified CUSUM Tests," Discussion Papers 2017-05, Graduate School of Economics, Hitotsubashi University.
    • Handle: RePEc:hit:econdp:2017-05
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    File URL: https://hermes-ir.lib.hit-u.ac.jp/hermes/ir/re/28728/070econDP17-05.pdf
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    References listed on IDEAS

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    1. Ploberger, Werner & Krämer;, Walter, 1990. "The Local Power of the CUSUM and CUSUM of Squares Tests," Econometric Theory, Cambridge University Press, vol. 6(3), pages 335-347, September.
    2. 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.
    3. Luger, Richard, 2001. "A modified CUSUM test for orthogonal structural changes," Economics Letters, Elsevier, vol. 73(3), pages 301-306, December.
    4. Juhl, Ted & Xiao, Zhijie, 2009. "Tests for changing mean with monotonic power," Journal of Econometrics, Elsevier, vol. 148(1), pages 14-24, January.
    5. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    6. Ploberger, Werner & Kramer, Walter, 1992. "The CUSUM Test with OLS Residuals," Econometrica, Econometric Society, vol. 60(2), pages 271-285, March.
    7. Jingjing Yang & Timothy J. Vogelsang, 2011. "Fixed‐b analysis of LM‐type tests for a shift in mean," Econometrics Journal, Royal Economic Society, vol. 14(3), pages 438-456, October.
    8. Kejriwal, Mohitosh, 2009. "Tests for a mean shift with good size and monotonic power," Economics Letters, Elsevier, vol. 102(2), pages 78-82, February.
    9. Shao, Xiaofeng & Zhang, Xianyang, 2010. "Testing for Change Points in Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1228-1240.
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    Cited by:

    1. Gabriela Ciuperca, 2022. "Real-time detection of a change-point in a linear expectile model," Statistical Papers, Springer, vol. 63(4), pages 1323-1367, August.

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