IDEAS home Printed from https://ideas.repec.org/p/bos/wpaper/wp2007-019.html
   My bibliography  Save this paper

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

Author

Listed:
  • Ai Deng

    () (Bates White, LLC)

  • Pierre Perron

    () (Department of Economics, Boston University)

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.

Suggested Citation

  • Ai Deng & Pierre Perron, 2007. "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 WP2007-019, Boston University - Department of Economics.
  • Handle: RePEc:bos:wpaper:wp2007-019
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ploberger, Werner & Krämer;, Walter, 1990. "The Local Power of the CUSUM and CUSUM of Squares Tests," Econometric Theory, Cambridge University Press, vol. 6(3), pages 335-347, September.
    2. Nigar Hashimzade & Timothy J. Vogelsang, 2008. "Fixed‐b asymptotic approximation of the sampling behaviour of nonparametric spectral density estimators," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(1), pages 142-162, January.
    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. 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.
    5. 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(3), pages 809-822, June.
    6. 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 153-162, April.
    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. 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. 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.
    10. repec:cup:etheor:v:6:y:1990:i:3:p:335-47 is not listed on IDEAS
    11. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    12. Kramer, Walter & Ploberger, Werner & Alt, Raimund, 1988. "Testing for Structural Change in Dynamic Models," Econometrica, Econometric Society, vol. 56(6), pages 1355-1369, November.
    13. Ploberger, Werner & Kramer, Walter, 1992. "The CUSUM Test with OLS Residuals," Econometrica, Econometric Society, vol. 60(2), pages 271-285, March.
    14. B. P. M. McCabe & M. J. Harrison, 1980. "Testing the Constancy of Regression Relationships Over Time Using Least Squares Residuals," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(2), pages 142-148, June.
    15. 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.
    16. Chu, C.S.J. & Hornik, K. & Kuan, C.M., 1993. "Mosum Tests for Parameter Constancy," Papers 9319, Southern California - Department of Economics.
    17. Ploberger, Werner & Kramer, Walter, 1986. "On studentizing a test for structural change," Economics Letters, Elsevier, vol. 20(4), pages 341-344.
    18. Pierre Perron, 2005. "Dealing with Structural Breaks," Boston University - Department of Economics - Working Papers Series WP2005-017, Boston University - Department of Economics.
    19. 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 289-299, July.
    20. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Perron, Pierre & Yabu, Tomoyoshi, 2009. "Estimating deterministic trends with an integrated or stationary noise component," Journal of Econometrics, Elsevier, vol. 151(1), pages 56-69, July.
    2. 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.
    3. Ploberger, Werner & Kramer, Walter, 1996. "A trend-resistant test for structural change based on OLS residuals," Journal of Econometrics, Elsevier, vol. 70(1), pages 175-185, January.
    4. 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.
    5. Kuan, Chung-Ming, 1998. "Tests for changes in models with a polynomial trend," Journal of Econometrics, Elsevier, vol. 84(1), pages 75-91, May.
    6. Anatolyev Stanislav & Kosenok Grigory, 2018. "Sequential Testing with Uniformly Distributed Size," Journal of Time Series Econometrics, De Gruyter, vol. 10(2), pages 1-22, July.
    7. Sven Otto & Jorg Breitung, 2020. "Backward CUSUM for Testing and Monitoring Structural Change," Papers 2003.02682, arXiv.org.
    8. Sahbi FARHANI, 2012. "Tests of Parameters Instability: Theoretical Study and Empirical Analysis on Two Types of Models (ARMA Model and Market Model)," International Journal of Economics and Financial Issues, Econjournals, vol. 2(3), pages 246-266.
    9. 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(3), pages 809-822, June.
    10. Altissimo, Filippo & Corradi, Valentina, 2003. "Strong rules for detecting the number of breaks in a time series," Journal of Econometrics, Elsevier, vol. 117(2), pages 207-244, December.
    11. Jamie Emerson & Chihwa Kao, 2000. "Testing for Structural Change of a Time Trend Regression in Panel Data," Center for Policy Research Working Papers 15, Center for Policy Research, Maxwell School, Syracuse University.
    12. Otto, Sven & Breitung, Jörg, 2020. "Backward CUSUM for Testing and Monitoring Structural Change," VfS Annual Conference 2020 (Virtual Conference): Gender Economics 224533, Verein für Socialpolitik / German Economic Association.
    13. Luis Fernando Melo Velandia & Martha Alicia Misas Arango, 2004. "Modelos Estructurales de Inflación en Colombia: Estimación a través de Mínimos Cuadrados Flexibles," BORRADORES DE ECONOMIA 003244, BANCO DE LA REPÚBLICA.
    14. Luger, Richard, 2001. "A modified CUSUM test for orthogonal structural changes," Economics Letters, Elsevier, vol. 73(3), pages 301-306, December.
    15. Raffaella Giacomini & Barbara Rossi, 2010. "Forecast comparisons in unstable environments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 595-620.
    16. Bilke, L., 2005. "Break in the Mean and Persistence of Inflation: a Sectoral Analysis of French CPI," Working papers 122, Banque de France.
    17. Xu, Ke-Li, 2013. "Powerful tests for structural changes in volatility," Journal of Econometrics, Elsevier, vol. 173(1), pages 126-142.
    18. Burcu Kapar & William Pouliot, 2013. "Multiple Change-Point Detection in Linear Regression Models via U-Statistic Type Processes," Discussion Papers 13-13, Department of Economics, University of Birmingham.
    19. Wu, Jilin, 2016. "A test for changing trends with monotonic power," Economics Letters, Elsevier, vol. 141(C), pages 15-19.
    20. Quintos, Carmela E., 1998. "Stability tests in error correction models," Journal of Econometrics, Elsevier, vol. 82(2), pages 289-315, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bos:wpaper:wp2007-019. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Program Coordinator). General contact details of provider: http://edirc.repec.org/data/decbuus.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.