IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

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

Author Info

Listed author(s):
  • 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.

Download Info

To our knowledge, this item is not available for download. To find whether it is available, there are three options:
1. Check below under "Related research" 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.

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

as
in new window

Length: 39pages
Date of creation: Mar 2007
Handle: RePEc:bos:wpaper:wp2007-019
Contact details of provider: Postal:
270 Bay State Road, Boston, MA 02215

Phone: 617-353-4389
Fax: 617-353-4449
Web page: http://www.bu.edu/econ/

More information through EDIRC

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

Other versions of this item:

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.:

as
in new window


  1. 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.
  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, 01.
  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(03), 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. 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.
  15. Chu, C.S.J. & Hornik, K. & Kuan, C.M., 1993. "Mosum Tests for Parameter Constancy," Papers 9319, Southern California - Department of Economics.
  16. Ploberger, Werner & Kramer, Walter, 1986. "On studentizing a test for structural change," Economics Letters, Elsevier, vol. 20(4), pages 341-344.
  17. Pierre Perron, 2005. "Dealing with Structural Breaks," Boston University - Department of Economics - Working Papers Series WP2005-017, Boston University - Department of Economics.
  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 289-299, 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.
Full references (including those not matched with items on IDEAS)

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

as
in new window


Cited by:
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page.

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Access and download statistics

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: (Gillian Gurish)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.