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Tests for Changing Mean with Monotonic Power

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  • 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.

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Bibliographic Info

Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 709.

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Length: 34 pages
Date of creation: 17 Jun 2009
Date of revision:
Handle: RePEc:boc:bocoec:709

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Keywords: stability; changing parameters; time varying parameters;

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References

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  1. Ploberger, Werner & Kramer, Walter, 1992. "The CUSUM Test with OLS Residuals," Econometrica, Econometric Society, vol. 60(2), pages 271-85, March.
  2. 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.
  3. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-56, July.
  4. Ai Deng & Pierre Perron, 2005. "A Non-local Perspective on the Power Properties of the CUSUM and CUSUM of Squares Tests for Structural Change," Boston University - Department of Economics - Working Papers Series WP2005-047, Boston University - Department of Economics.
  5. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  6. Li, Qi, 1999. "Consistent model specification tests for time series econometric models," Journal of Econometrics, Elsevier, vol. 92(1), pages 101-147, September.
  7. Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation for Research in Economics, Yale University.
  8. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1449-1459, December.
  9. Graham Elliott & Ulrich K. M�ller, 2006. "Efficient Tests for General Persistent Time Variation in Regression Coefficients -super-1," Review of Economic Studies, Oxford University Press, vol. 73(4), pages 907-940.
  10. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
  11. 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.
  12. Hansen, Bruce E, 1992. "Tests for Parameter Instability in Regressions with I(1) Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 321-35, July.
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Cited by:
  1. 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.
  2. Xu, Ke-Li, 2013. "Power monotonicity in detecting volatility levels change," Economics Letters, Elsevier, vol. 121(1), pages 64-69.
  3. Xu, Ke-Li, 2013. "Powerful tests for structural changes in volatility," Journal of Econometrics, Elsevier, vol. 173(1), pages 126-142.

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