Testing For A Unit Root In The Presence Of A Possible Break In Trend
Abstract
In this paper we consider the issue of testing a time series for a unit root in the possible presence of a break in a linear deterministic trend at some unknown point in the series. We propose a break fraction estimator which, in the presence of a break in trend, is consistent for the true break fraction at rate Op(T^-1) when there is either a unit root or near-unit root in the stochastic component of the series. In contrast to other estimators available in the literature, when there is no break in trend, our proposed break fraction estimator converges to zero at rate Op(T^-1/2). Used in conjunction with a quasi difference (QD) detrended unit root test that incorporates a trend break regressor in the deterministic component, we show that these rates of convergence ensure that known break fraction null critical values are applicable asymptotically. Unlike available procedures in the literature this holds even if there is no break in trend (the true break fraction is zero), in which case the trend break regressor is dropped from the deterministic component and standard QD detrended unit root test critical values then apply. We also propose a second testing procedure which makes use of a formal pre-test for a trend break in the series, including a trend break regressor only where the pre-test rejects the null of no break. Both procedures ensure that the correctly sized (near-) efficient unit root test that allows (does not allow) for a break in trend is applied in the limit when a trend break does (does not) occur.(This abstract was borrowed from another version of this item.)
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Article provided by Cambridge University Press in its journal Econometric Theory.
Volume (Year): 25 (2009)
Issue (Month): 06 (December)
Pages: 1545-1588
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Keywords:Other versions of this item:
- David Harris & David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2007. "Testing for a unit root in the presence of a possible break in trend," Discussion Papers 07/04, University of Nottingham, Granger Centre for Time Series Econometrics.
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Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.Cited by:
- David I. Harvey, & Stephen J. Leybourne, & A. M. Robert Taylor, 2007. "Testing for a unit root when uncertain about the trend [Revised to become 07/03 above]," Discussion Papers 06/03, University of Nottingham, Granger Centre for Time Series Econometrics.
- Richard S. J. Tol & Francisco Estrada & Carlos Gay-García, 2012. "The persistence of shocks in GDP and the estimation of the potential economic costs of climate change," Working Paper Series 4312, Department of Economics, University of Sussex.
- Giuseppe Cavaliere & David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2009.
"Testing for unit roots in the presence of a possible break in trend and non-stationary volatility,"
Discussion Papers
09/05, University of Nottingham, Granger Centre for Time Series Econometrics.
- Cavaliere, Giuseppe & Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2011. "Testing For Unit Roots In The Presence Of A Possible Break In Trend And Nonstationary Volatility," Econometric Theory, Cambridge University Press, vol. 27(05), pages 957-991, October.
- Giuseppe Cavaliere & David I. Harvey & Stephen J. Leybourne & A.M. Robert Taylor, 2008. "Testing for Unit Roots in the Presence of a Possible Break in Trend and Non-Stationary Volatility," CREATES Research Papers 2008-62, School of Economics and Management, University of Aarhus.
- Pitarakis, Jean-Yves, 2011. "Joint Detection of Structural Change and Nonstationarity in Autoregressions," MPRA Paper 29189, University Library of Munich, Germany.
- Mohitosh Kejriwal & Claude Lopez, 2010.
"Unit Roots, Level Shifts and Trend Breaks in PerCapita Output: A Robust Evaluation,"
University of Cincinnati, Economics Working Papers Series
2010-02, University of Cincinnati, Department of Economics.
- Mohitosh Kejriwal & Claude Lopez, 2009. "Unit Roots, Level Shifts and Trend Breaks in Per Capita Output: A Robust Evaluation," Purdue University Economics Working Papers 1227, Purdue University, Department of Economics.
- Kejriwal , M. & Lopez, C., 2011. "Unit Roots, Level Shifts and Trend Breaks in Per Capita Output: A Robust Evaluation," Working papers 334, Banque de France.
- Kejriwal, Mohitosh & Lopez, Claude, 2010. "Unit Roots, Level Shifts and Trend Breaks in Per Capita Output: A Robust Evaluation," MPRA Paper 25204, University Library of Munich, Germany.
- Ghoshray, Atanu & Kejriwal, Mohitosh & Wohar, Mark E., 2011. "Breaking Trends and the Prebisch-Singer Hypothesis: A Further Investigation," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 120387, European Association of Agricultural Economists.
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"Unit Root Testing In Practice: Dealing With Uncertainty Over The Trend And Initial Condition,"
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Cambridge University Press, vol. 25(03), pages 587-636, June.
- David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2007. "Unit root testing in practice: dealing with uncertainty over the trend and initial condition," Discussion Papers 07/03, University of Nottingham, Granger Centre for Time Series Econometrics.
- Fossati, Sebastian, 2011. "Unit Root Testing with Stationary Covariates and a Structural Break in the Trend Function," Working Papers 2011-10, University of Alberta, Department of Economics.
- Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2012. "Unit roots, nonlinearities and structural breaks," CREATES Research Papers 2012-14, School of Economics and Management, University of Aarhus.
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