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Iacone, Fabrizio and Leybourne, Stephen J and Taylor, AM Robert (2013) 'ON THE BEHAVIOR OF FIXED-<i>b</i> TREND BREAK TESTS UNDER FRACTIONAL INTEGRATION.' Econometric Theory, 29 (2). pp. 393-418. ISSN 0266-4666

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<jats:p>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, <jats:italic>Econometric Theory</jats:italic> 27, 992–1025) (SV) show that tests based on fixed-<jats:italic>b</jats:italic> 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-<jats:italic>b</jats:italic> 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 <jats:italic>δ</jats:italic>. As a result, it is only when <jats:italic>δ</jats:italic> is either zero or one that the SV critical values yield correctly sized tests. Consequently, we propose a procedure that employs <jats:italic>δ</jats:italic>-adaptive critical values to remove the size distortions in the SV test. In addition, use of <jats:italic>δ</jats:italic>-adaptive critical values also allows us to consider a simplification of the SV test that is (asymptotically) correctly sized across <jats:italic>δ</jats:italic> but can also provide a significant increase in power over the standard SV test when <jats:italic>δ</jats:italic> = 1.</jats:p>

Item Type: Article
Subjects: H Social Sciences > HG Finance
Divisions: Faculty of Social Sciences
Faculty of Social Sciences > Essex Business School
Faculty of Social Sciences > Essex Business School > Essex Finance Centre
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 17 Nov 2014 12:49
Last Modified: 12 Apr 2022 18:40

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