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Tests for Changing Mean with Monotonic Power

Author

Listed:
  • Ted Juhl

    (University of Kansas)

  • Zhijie Xiao

    (Boston College)

Abstract

Several widely used tests for a changing mean exhibit nonmonotonic power in finite samples due to "incorrect" estimation of nuisance parameters under the alternative. In this paper, we study the issue of nonmonotonic power in testing for changing mean. We investigate the asymptotic power properties of the tests using a new framework where alternatives are characterized as having "large" changes. The asymptotic analysis provides a theoretical explanation to the power problem. Modified tests that have monotonic power against a wide range of alternatives of structural change are proposed. Instead of estimating the nuisance parameters based on ordinary least squares residuals, the proposed tests use modified estimators based on nonparametric regression residuals. It is shown that tests based on the modified long-run variance estimator provide an improved rate of divergence of the tests under the alternative of a change in mean. Tests for structural breaks based on such an estimator are able to remain consistent while still retaining the same asymptotic distribution under the null hypothesis of constant mean.

Suggested Citation

  • Ted Juhl & Zhijie Xiao, 2009. "Tests for Changing Mean with Monotonic Power," Boston College Working Papers in Economics 709, Boston College Department of Economics.
    • Handle: RePEc:boc:bocoec:709
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    References listed on IDEAS

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    Cited by:

    1. Xu, Ke-Li, 2013. "Power monotonicity in detecting volatility levels change," Economics Letters, Elsevier, vol. 121(1), pages 64-69.
    2. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    3. YAMAZAKI, Daisuke & 山崎, 大輔 & KUROZUMI, Eiji & 黒住, 英司, 2014. "Improving the Finite Sample Performance of Tests for a Shift in Mean," Discussion Papers 2014-16, Graduate School of Economics, Hitotsubashi University.
    4. Wu, Jilin, 2016. "A test for changing trends with monotonic power," Economics Letters, Elsevier, vol. 141(C), pages 15-19.
    5. Górecki, Tomasz & Horváth, Lajos & Kokoszka, Piotr, 2018. "Change point detection in heteroscedastic time series," Econometrics and Statistics, Elsevier, vol. 7(C), pages 63-88.
    6. Ping‐Shou Zhong, 2023. "Homogeneity tests of covariance for high‐dimensional functional data with applications to event segmentation," Biometrics, The International Biometric Society, vol. 79(4), pages 3332-3344, December.
    7. Ke-Li Xu & Jui-Chung Yang, 2015. "Towards Uniformly Efficient Trend Estimation Under Weak/Strong Correlation and Non-stationary Volatility," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 63-86, March.
    8. Jean-Yves Pitarakis, 2017. "A Simple Approach for Diagnosing Instabilities in Predictive Regressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(5), pages 851-874, October.
    9. Alexander Ludwig, 2013. "Testing the null of cointegration with a structural break: optimal kernel and bandwidth selection," Economics Bulletin, AccessEcon, vol. 33(4), pages 2828-2839.
    10. Grote, Claudia & Bertram, Philip, 2015. "A comparative Study of Volatility Breaks," Hannover Economic Papers (HEP) dp-558, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    11. Peiyun Jiang & Eiji Kurozumi, 2019. "Power properties of the modified CUSUM tests," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(12), pages 2962-2981, June.
    12. Pierre Perron & Yohei Yamamoto, 2016. "On the Usefulness or Lack Thereof of Optimality Criteria for Structural Change Tests," Econometric Reviews, Taylor & Francis Journals, vol. 35(5), pages 782-844, May.
    13. Xu, Ke-Li, 2013. "Powerful tests for structural changes in volatility," Journal of Econometrics, Elsevier, vol. 173(1), pages 126-142.
    14. Wu, Jilin, 2015. "Restoring monotonic power in Wald/LM-type tests," Economics Letters, Elsevier, vol. 126(C), pages 13-17.
    15. Chen, Zhihong & Xia, Huizhu, 2020. "Trend instrumental variable regression with an application to the US New Keynesian Phillips Curve," Economic Modelling, Elsevier, vol. 93(C), pages 595-604.
    16. Li, Zheng & Su, Li & Zhang, Daiqiang, 2014. "Profile least squares estimation of a partially linear time trend model with weakly dependent data," Economics Letters, Elsevier, vol. 125(3), pages 404-407.
    17. Lee, Taewook & Baek, Changryong, 2020. "Block wild bootstrap-based CUSUM tests robust to high persistence and misspecification," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).

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    More about this item

    Keywords

    stability; changing parameters; time varying parameters;
    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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