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SIMPLE, ROBUST, AND POWERFUL TESTS OF THE BREAKING TREND HYPOTHESIS

Published online by Cambridge University Press:  01 August 2009

David I. Harvey ,
Stephen J. Leybourne  and
A.M. Robert Taylor
David I. Harvey
Affiliation:
Granger Centre for Time Series Econometrics University of Nottingham
Stephen J. Leybourne
Affiliation:
Granger Centre for Time Series Econometrics University of Nottingham
A.M. Robert Taylor*
Affiliation:
Granger Centre for Time Series Econometrics University of Nottingham
*
*Correspondence to: Robert Taylor, School of Economics, University of Nottingham, University Park, Nottingham, NG7 2RD, U.K; e-mail: [email protected].
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Abstract

In this paper we develop a simple procedure that delivers tests for the presence of a broken trend in a univariate time series that do not require knowledge of the form of serial correlation in the data and are robust as to whether the shocks are generated by an I(0) or an I(1) process. Two trend break models are considered: the first holds the level fixed while allowing the trend to break, while the latter allows for a simultaneous break in level and trend. For the known break date case, our proposed tests are formed as a weighted average of the optimal tests appropriate for I(0) and I(1) shocks. The weighted statistics are shown to have standard normal limiting null distributions and to attain the Gaussian asymptotic local power envelope, in each case regardless of whether the shocks are I(0) or I(1). In the unknown break date case, we adopt the method of Andrews (1993) and take a weighted average of the statistics formed as the supremum over all possible break dates, subject to a trimming parameter, in both the I(0) and I(1) environments. Monte Carlo evidence suggests that our tests are in most cases more powerful, often substantially so, than the robust broken trend tests of Sayginsoy and Vogelsang (2004). An empirical application highlights the practical usefulness of our proposed tests.

Type
ARTICLES
Information
Econometric Theory , Volume 25 , Issue 4: Bergstrom Memorial Dedication Issue , August 2009 , pp. 995 - 1029
Copyright
Copyright © Cambridge University Press 2009

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