IDEAS home Printed from https://ideas.repec.org/p/boc/bocoec/709.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: http://fmwww.bc.edu/EC-P/wp709.pdf
    File Function: main text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. Li, Qi, 1999. "Consistent model specification tests for time series econometric models," Journal of Econometrics, Elsevier, vol. 92(1), pages 101-147, September.
    3. Hsiao, Cheng & Li, Qi, 2001. "A Consistent Test For Conditional Heteroskedasticity In Time-Series Regression Models," Econometric Theory, Cambridge University Press, vol. 17(1), pages 188-221, February.
    4. Graham Elliott & Ulrich K. Muller, 2006. "Efficient Tests for General Persistent Time Variation in Regression Coefficients," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(4), pages 907-940.
    5. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    6. Ploberger, Werner & Kramer, Walter, 1992. "The CUSUM Test with OLS Residuals," Econometrica, Econometric Society, vol. 60(2), pages 271-285, March.
    7. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    8. Hansen, Bruce E, 2002. "Tests for Parameter Instability in Regressions with I(1) Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 45-59, January.
    9. 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.
    10. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    11. Vogelsang, Timothy J., 1998. "Sources of nonmonotonic power when testing for a shift in mean of a dynamic time series," Journal of Econometrics, Elsevier, vol. 88(2), pages 283-299, November.
    12. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1449-1459, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Wu, Jilin, 2015. "Restoring monotonic power in Wald/LM-type tests," Economics Letters, Elsevier, vol. 126(C), pages 13-17.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Xu, Ke-Li, 2013. "Power monotonicity in detecting volatility levels change," Economics Letters, Elsevier, vol. 121(1), pages 64-69.
    9. 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.
    10. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    11. 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.
    12. Grote, Claudia & Bertram, Philip, 2015. "A comparative Study of Volatility Breaks," Hannover Economic Papers (HEP) dp-558, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    13. 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.
    14. Xu, Ke-Li, 2013. "Powerful tests for structural changes in volatility," Journal of Econometrics, Elsevier, vol. 173(1), pages 126-142.
    15. 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).
    16. Wu, Jilin, 2016. "A test for changing trends with monotonic power," Economics Letters, Elsevier, vol. 141(C), pages 15-19.
    17. Górecki, Tomasz & Horváth, Lajos & Kokoszka, Piotr, 2018. "Change point detection in heteroscedastic time series," Econometrics and Statistics, Elsevier, vol. 7(C), pages 63-88.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Boston University - Department of Economics - Working Papers Series WP2019-02, Boston University - Department of Economics.
    3. 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.
    4. Abhimanyu Gupta & Myung Hwan Seo, 2023. "Robust Inference on Infinite and Growing Dimensional Time‐Series Regression," Econometrica, Econometric Society, vol. 91(4), pages 1333-1361, July.
    5. Rossi, Barbara, 2013. "Advances in Forecasting under Instability," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1203-1324, Elsevier.
    6. Andersen, Torben G. & Varneskov, Rasmus T., 2022. "Testing for parameter instability and structural change in persistent predictive regressions," Journal of Econometrics, Elsevier, vol. 231(2), pages 361-386.
    7. Yamamoto, Yohei & Tanaka, Shinya, 2015. "Testing for factor loading structural change under common breaks," Journal of Econometrics, Elsevier, vol. 189(1), pages 187-206.
    8. Alaa Abi Morshed & Elena Andreou & Otilia Boldea, 2018. "Structural Break Tests Robust to Regression Misspecification," Econometrics, MDPI, vol. 6(2), pages 1-39, May.
    9. Alessandro Casini, 2018. "Tests for Forecast Instability and Forecast Failure under a Continuous Record Asymptotic Framework," Papers 1803.10883, arXiv.org, revised Dec 2018.
    10. 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.
    11. Elliott, Graham & Muller, Ulrich K., 2007. "Confidence sets for the date of a single break in linear time series regressions," Journal of Econometrics, Elsevier, vol. 141(2), pages 1196-1218, December.
    12. Chen, Shiu-Sheng & Chou, Yu-Hsi, 2015. "Revisiting the relationship between exchange rates and fundamentals," Journal of Macroeconomics, Elsevier, vol. 46(C), pages 1-22.
    13. Xu, Ke-Li, 2013. "Powerful tests for structural changes in volatility," Journal of Econometrics, Elsevier, vol. 173(1), pages 126-142.
    14. Strauss, Jack & Yigit, Taner, 2001. "Present value model, heteroscedasticity and parameter stability tests," Economics Letters, Elsevier, vol. 73(3), pages 375-378, December.
    15. Vogelsang, Timothy J., 1998. "Sources of nonmonotonic power when testing for a shift in mean of a dynamic time series," Journal of Econometrics, Elsevier, vol. 88(2), pages 283-299, November.
    16. Raffaella Giacomini & Barbara Rossi, 2015. "Forecasting in Nonstationary Environments: What Works and What Doesn't in Reduced-Form and Structural Models," Annual Review of Economics, Annual Reviews, vol. 7(1), pages 207-229, August.
    17. Zeileis, Achim, 2006. "Implementing a class of structural change tests: An econometric computing approach," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 2987-3008, July.
    18. Oka, Tatsushi & Perron, Pierre, 2018. "Testing for common breaks in a multiple equations system," Journal of Econometrics, Elsevier, vol. 204(1), pages 66-85.
    19. Mehmet Balcilar & Rangan Gupta & Stephen M. Miller, 2014. "Housing and the Great Depression," Applied Economics, Taylor & Francis Journals, vol. 46(24), pages 2966-2981, August.
    20. Kejriwal, Mohitosh & Perron, Pierre, 2010. "Testing for Multiple Structural Changes in Cointegrated Regression Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 503-522.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:boc:bocoec:709. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Christopher F Baum (email available below). General contact details of provider: https://edirc.repec.org/data/debocus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.