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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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  • Deng, Ai
  • Perron, Pierre

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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 142 (2008)
Issue (Month): 1 (January)
Pages: 212-240

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Handle: RePEc:eee:econom:v:142:y:2008:i:1:p:212-240

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Web page: http://www.elsevier.com/locate/jeconom

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  1. repec:cup:etheor:v:6:y:1990:i:3:p:335-47 is not listed on IDEAS
  2. Ploberger, Werner & Kramer, Walter, 1992. "The CUSUM Test with OLS Residuals," Econometrica, Econometric Society, vol. 60(2), pages 271-85, March.
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Citations

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Cited by:
  1. Nielsen, Bent & Sohkanen, Jouni S., 2011. "Asymptotic Behavior Of The Cusum Of Squares Test Under Stochastic And Deterministic Time Trends," Econometric Theory, Cambridge University Press, vol. 27(04), pages 913-927, August.
  2. Xu, Ke-Li, 2013. "Powerful tests for structural changes in volatility," Journal of Econometrics, Elsevier, vol. 173(1), pages 126-142.
  3. Paulo M.M. Rodrigues & Antonio Rubia, 2010. "The Effects of Additive Outliers and Measurement Errors when Testing for Structural Breaks in Variance," Working Papers w201011, Banco de Portugal, Economics and Research Department.
  4. Jin Seo Cho & Halbert White, 2009. "Generalized Runs Test for the IID Hypothesis," Discussion Paper Series 0913, Institute of Economic Research, Korea University.
  5. Kim, Dukpa & Perron, Pierre, 2009. "Assessing the relative power of structural break tests using a framework based on the approximate Bahadur slope," Journal of Econometrics, Elsevier, vol. 149(1), pages 26-51, April.
  6. Pierre Perron & Yohei Yamamoto, 2012. "On the Usefulness or Lack Thereof of Optimality Criteria for Structural Change Tests," Global COE Hi-Stat Discussion Paper Series gd12-258, Institute of Economic Research, Hitotsubashi University.
  7. 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.
  8. 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.
  9. Kejriwal, Mohitosh, 2009. "Tests for a mean shift with good size and monotonic power," Economics Letters, Elsevier, vol. 102(2), pages 78-82, February.
  10. Xu, Ke-Li, 2013. "Power monotonicity in detecting volatility levels change," Economics Letters, Elsevier, vol. 121(1), pages 64-69.
  11. YAMAMOTO, Yohei & TANAKA, Shinya, 2013. "Testing for Factor Loading Structural Change under Common Breaks," Discussion Papers 2013-17, Graduate School of Economics, Hitotsubashi University.

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