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ON THE BEHAVIOR OF FIXED-b TREND BREAK TESTS UNDER FRACTIONAL INTEGRATION

Published online by Cambridge University Press:  06 July 2012

Fabrizio Iacone ,
Stephen J. Leybourne  and
A.M. Robert Taylor
Fabrizio Iacone
Affiliation:
University of York
Stephen J. Leybourne
Affiliation:
University of Nottingham
A.M. Robert Taylor*
Affiliation:
University of Nottingham
*
*Address correspondence to Robert Taylor, School of Economics, The Sir Clive Granger Building, University of Nottingham, Nottingham NG7 2RD, United Kingdom; e-mail: Robert.Taylor@nottingham.ac.uk.
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Abstract

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.

Information

Type
Miscellanea
Information
Econometric Theory , Volume 29 , Issue 2 , April 2013 , pp. 393 - 418
Copyright
Copyright © Cambridge University Press 2012 

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Footnotes

We thank the editor, a co-editor, and two anonymous referees for their helpful and constructive comments on earlier versions of this paper. We also thank participants at the conference in honor of Sir David F. Hendry held at St. Andrews University on 22–23 July 2010 for their comments.

References

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