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Tests for Changing Mean with Monotonic Power


  • Ted Juhl

    () (University of Kansas)

  • Zhijie Xiao

    () (Boston College)


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

    1. 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.
    2. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    3. 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.
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    5. Li, Qi, 1999. "Consistent model specification tests for time series econometric models," Journal of Econometrics, Elsevier, vol. 92(1), pages 101-147, September.
    6. Graham Elliott & Ulrich K. Muller, 2006. "Efficient Tests for General Persistent Time Variation in Regression Coefficients," Review of Economic Studies, Oxford University Press, vol. 73(4), pages 907-940.
    7. 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.
    8. 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.
    9. Hsiao, Cheng & Li, Qi, 2001. "A Consistent Test For Conditional Heteroskedasticity In Time-Series Regression Models," Econometric Theory, Cambridge University Press, vol. 17(01), pages 188-221, February.
    10. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    11. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1449-1459, December.
    12. Ploberger, Werner & Kramer, Walter, 1992. "The CUSUM Test with OLS Residuals," Econometrica, Econometric Society, vol. 60(2), pages 271-285, March.
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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. Xu, Ke-Li, 2013. "Powerful tests for structural changes in volatility," Journal of Econometrics, Elsevier, vol. 173(1), pages 126-142.
    3. Wu, Jilin, 2016. "A test for changing trends with monotonic power," Economics Letters, Elsevier, vol. 141(C), pages 15-19.
    4. Wu, Jilin, 2015. "Restoring monotonic power in Wald/LM-type tests," Economics Letters, Elsevier, vol. 126(C), pages 13-17.
    5. 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.
    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. repec:bla:obuest:v:79:y:2017:i:5:p:851-874 is not listed on IDEAS
    8. 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.
    9. Grote, Claudia & Bertram, Philip, 2015. "A comparative Study of Volatility Breaks," Hannover Economic Papers (HEP) dp-558, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    10. JIANG, Peiyun & KUROZUMI, Eiji, 2017. "Power Properties of the Modified CUSUM Tests," Discussion Papers 2017-05, Graduate School of Economics, Hitotsubashi University.
    11. Yichen Gao & Zheng Li & Zhongjian Lin, 2014. "Semiparametric Estimation of Partially Linear Varying Coefficient Models with Time Trend and Nonstationary Regressors," Emory Economics 1412, Department of Economics, Emory University (Atlanta).

    More about this item


    stability; changing parameters; time varying parameters;

    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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