IDEAS home Printed from
   My bibliography  Save this article



  • Iacone, Fabrizio
  • Leybourne, Stephen J.
  • Taylor, A.M. Robert


Testing for the presence of a broken linear trend when the nature of the persistence in the data is unknown is not a trivial problem, because the test needs to be both asymptotically correctly sized and consistent, regardless of the order of integration of the data. In a recent paper, Sayginsoy and Vogelsang (2011, Econometric Theory 27, 992–1025) (SV) show that tests based on fixed- b asymptotics provide a useful solution to this problem in the case where the shocks may be either weakly dependent or display strong dependence within the near-unit-root class. In this paper we analyze the performance of these tests when the shocks may be fractionally integrated, an alternative model paradigm that allows for either weak or strong dependence in the shocks. We demonstrate that the fixed- b trend break statistics converge to well-defined limit distributions under both the null and local alternatives in this case (and retain consistency against fixed alternatives), but that these distributions depend on the fractional integration parameter δ . As a result, it is only when δ is either zero or one that the SV critical values yield correctly sized tests. Consequently, we propose a procedure that employs δ -adaptive critical values to remove the size distortions in the SV test. In addition, use of δ -adaptive critical values also allows us to consider a simplification of the SV test that is (asymptotically) correctly sized across δ but can also provide a significant increase in power over the standard SV test when δ = 1.

Suggested Citation

  • Iacone, Fabrizio & Leybourne, Stephen J. & Taylor, A.M. Robert, 2013. "ON THE BEHAVIOR OF FIXED-b TREND BREAK TESTS UNDER FRACTIONAL INTEGRATION," Econometric Theory, Cambridge University Press, vol. 29(02), pages 393-418, April.
  • Handle: RePEc:cup:etheor:v:29:y:2013:i:02:p:393-418_00

    Download full text from publisher

    File URL:
    File Function: link to article abstract page
    Download Restriction: no

    Other versions of this item:


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

    Cited by:

    1. Fabrizio Iacone & Stephen J. Leybourne & A. M. Robert Taylor, 2014. "A FIXED- b TEST FOR A BREAK IN LEVEL AT AN UNKNOWN TIME UNDER FRACTIONAL INTEGRATION," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(1), pages 40-54, January.
    2. Bent Jesper Christensen & Robinson Kruse & Philipp Sibbertsen, 2013. "A unified framework for testing in the linear regression model under unknown order of fractional integration," CREATES Research Papers 2013-35, Department of Economics and Business Economics, Aarhus University.
    3. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807,
    4. Javier Hualde & Fabrizio Iacone, 2015. "Small-b and Fixed-b Asymptotics for Weighted Covariance Estimation in Fractional Cointegration," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(4), pages 528-540, July.

    More about this item


    Access and download statistics


    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:cup:etheor:v:29:y:2013:i:02:p:393-418_00. 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: (Keith Waters). General contact details of provider: .

    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.

    We have no references for this item. You can help adding them by using 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.