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A Non-local Perspective on the Power Properties of the CUSUM and CUSUM of Squares Tests for Structural Change

  • Ai Deng

    ()

    (Bates White, LLC)

  • Pierre Perron

    ()

    (Department of Economics, Boston University)

We consider the power properties of the CUSUM and CUSUM of squares tests in the presence of a one-time change in the parameters of a linear regression model. A result due to Ploberger and Krämer (1990) is that the CUSUM of squares test has only trivial asymptotic local power in this case, while the CUSUM test has non-trivial local asymptotic power unless the change is orthogonal to the mean regressor. The main theme of the paper is that such conclusions obtained from a local asymptotic framework are not reliable guides to what happens in finite samples. The approach we take is to derive expansions of the test statistics that retain terms related to the magnitude of the change under the alternative hypothesis. This enables us to analyze what happens for non-local to zero breaks. Our theoretical results are able to explain how the power function of the tests can be drastically different depending on whether one deals with a static regression with uncorrelated errors, a static regression with correlated errors, a dynamic regression with lagged dependent variables, or whether a correction for non-Normality is applied in the case of the CUSUM of squares. We discuss in which cases the tests are subject to a non-monotonic power function that goes to zero as the magnitude of the change increases, and uncover some curious properties. All theoretical results are verified to yield good guides to the finite sample power through simulation experiments. We finally highlight the practical importance of our results.

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Paper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number WP2007-019.

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Length: 39pages
Date of creation: Mar 2007
Date of revision:
Handle: RePEc:bos:wpaper:wp2007-019
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Web page: http://www.bu.edu/econ/

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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. Ai Deng & Pierre Perron, 2006. "The Limit Distribution of the CUSUM of Squares Test Under General Mixing Conditions," Boston University - Department of Economics - Working Papers Series wp2006-004, Boston University - Department of Economics.
  3. Peter Phillips & Hyungsik Moon, 2000. "Nonstationary panel data analysis: an overview of some recent developments," Econometric Reviews, Taylor & Francis Journals, vol. 19(3), pages 263-286.
  4. Ploberger, Werner & Kramer, Walter, 1986. "On studentizing a test for structural change," Economics Letters, Elsevier, vol. 20(4), pages 341-344.
  5. Hashimzade, Nigar & Vogelsang, Timothy, 2006. "Fixed-b Asymptotic Approximation of the Sampling Behavior of Nonparametric Spectral Density Estimators," Working Papers 06-04, Cornell University, Center for Analytic Economics.
  6. Chu, Chia-Shang James & White, Halbert, 1992. "A Direct Test for Changing Trend," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 289-99, July.
  7. Crainiceanu, Ciprian & Vogelsang, Timothy, 2001. "Spectral Density Bandwidth Choice: Source of Nonmonotonic Power for Tests of a Mean Shift in a Time Series," Working Papers 01-14, Cornell University, Center for Analytic Economics.
  8. repec:cup:etheor:v:6:y:1990:i:3:p:335-47 is not listed on IDEAS
  9. Perron, P., 1989. "Testing For A Unit Root In A Time Series With A Changing Mean," Papers 347, Princeton, Department of Economics - Econometric Research Program.
  10. Perron, P., 1991. "A Test for Changes in a Polynomial Trend Functions for a Dynamioc Time Series," Papers 363, Princeton, Department of Economics - Econometric Research Program.
  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. Dufour, Jean-Marie, 1982. "Recursive stability analysis of linear regression relationships: An exploratory methodology," Journal of Econometrics, Elsevier, vol. 19(1), pages 31-76, May.
  13. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  14. Kramer, Walter & Ploberger, Werner & Alt, Raimund, 1988. "Testing for Structural Change in Dynamic Models," Econometrica, Econometric Society, vol. 56(6), pages 1355-69, November.
  15. Ploberger, Werner & Krämer;, Walter, 1990. "The Local Power of the CUSUM and CUSUM of Squares Tests," Econometric Theory, Cambridge University Press, vol. 6(03), pages 335-347, September.
  16. Pierre Perron, 2005. "Dealing with Structural Breaks," Boston University - Department of Economics - Working Papers Series WP2005-017, Boston University - Department of Economics.
  17. Ploberger, Werner & Kramer, Walter & Kontrus, Karl, 1989. "A new test for structural stability in the linear regression model," Journal of Econometrics, Elsevier, vol. 40(2), pages 307-318, February.
  18. Ai Deng & Pierre Perron, 2005. "The Limit Distribution of the CUSUM of Square Test Under Genreal MIxing Conditions," Boston University - Department of Economics - Working Papers Series WP2005-046, Boston University - Department of Economics.
  19. Chu, C.S.J. & Hornik, K. & Kuan, C.M., 1993. "Mosum Tests for Parameter Constancy," Papers 9319, Southern California - Department of Economics.
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