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

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Author Info
Ai Deng () (Bates White, LLC)
Pierre Perron () (Department of Economics, Boston University)

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Abstract

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
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Handle: RePEc:bos:wpaper:wp2007-019

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Related research
Keywords: Change-point; Mean shift; Local asymptotic power; Recursive residuals; Dynamic models.;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Ploberger, Werner & Kr?mer;, 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. [Downloadable!]
  2. Ploberger, Werner & Kramer, Walter, 1992. "The CUSUM Test with OLS Residuals," Econometrica, Econometric Society, vol. 60(2), pages 271-85, March. [Downloadable!] (restricted)
  3. repec:cup:etheor:v:6:y:1990:i:3:p:335-47 is not listed on IDEAS
  4. Chung-Ming Kuan & Kurt Hornik, 1995. "The generalized fluctuation test: A unifying view," Econometric Reviews, Taylor and Francis Journals, vol. 14(2), pages 135-161. [Downloadable!] (restricted)
  5. Nigar Hashimzade & Timothy J. Vogelsang, 2008. "Fixed-b asymptotic approximation of the sampling behaviour of nonparametric spectral density estimators," Journal of Time Series Analysis, Blackwell Publishing, vol. 29(1), pages 142-162, 01. [Downloadable!] (restricted)
    Other versions:
  6. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May. [Downloadable!] (restricted)
    Other versions:
  7. Kramer, Walter & Ploberger, Werner & Alt, Raimund, 1988. "Testing for Structural Change in Dynamic Models," Econometrica, Econometric Society, vol. 56(6), pages 1355-69, November. [Downloadable!] (restricted)
  8. Peter C.B. Phillips & Hyungsik R. Moon, 1999. "Nonstationary Panel Data Analysis: An Overview of Some Recent Developments," Cowles Foundation Discussion Papers 1221, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  9. Chu, C.S.J. & Hornik, K. & Kuan, C.M., 1993. "Mosum Tests for Parameter Constancy," Papers 9319, Southern California - Department of Economics.
  10. 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. [Downloadable!]
  11. Ploberger, Werner & Kramer, Walter, 1986. "On studentizing a test for structural change," Economics Letters, Elsevier, vol. 20(4), pages 341-344. [Downloadable!] (restricted)
  12. 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. [Downloadable!] (restricted)
  13. Pierre Perron, 2005. "Dealing with Structural Breaks," Boston University - Department of Economics - Working Papers Series WP2005-017, Boston University - Department of Economics. [Downloadable!]
  14. 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.
  15. Deng, Ai & Perron, Pierre, 2008. "The Limit Distribution Of The Cusum Of Squares Test Under General Mixing Conditions," Econometric Theory, Cambridge University Press, vol. 24(03), pages 809-822, June. [Downloadable!]
    Other versions:
  16. 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. [Downloadable!]
  17. Perron, Pierre, 1990. "Testing for a Unit Root in a Time Series with a Changing Mean," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 153-62, April.
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  18. 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.
  19. 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. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Dukpa Kim & Pierre Perron, 2006. "Assessing the Relative Power of Structural Break Tests Using a Framework Based on the Approximate Bahadur Slope," Boston University - Department of Economics - Working Papers Series WP2006-063, Boston University - Department of Economics. [Downloadable!]
    Other versions:
  2. Pierre Perron & Yohei Yamamoto, 2008. "On the Usefulness or Lack Thereof of Optimality Criteria for Structural Change Tests," Boston University - Department of Economics - Working Papers Series wp2008-006, Boston University - Department of Economics. [Downloadable!]
  3. Ted Juhl & Zhijie Xiao, 2008. "Tests For Changing Mean With Monotonic Power," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200809, University of Kansas, Department of Economics, revised Sep 2008. [Downloadable!]
  4. 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. [Downloadable!]
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