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Modified tests for a change in persistence

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  • Harvey, David I.
  • Leybourne, Stephen J.
  • Taylor, A.M. Robert

Abstract

Being able to correctly characterise an observed time series into its separate difference stationary and trend stationary regimes, should they exist, has important implications for effective model building and forecasting in economics and finance. Existing ratio-based statistics test the null hypothesis that a time series displays constant trend stationarity, I(0), against the alternative of a change in persistence from trend stationarity to difference stationarity, I(1), or vice versa. Here, however, we demonstrate that these tests are unable to adequately discern between a true change in persistence and a constant I(1) process. We propose modified tests which, by design, have the same critical values regardless of whether the process is I(0) or I(1) throughout. Hence, our null hypothesis is that of constant persistence (either constant I(0) or constant I(1)). Tests directed against both I(1) to I(0) and I(0) to I(1) persistence changes are provided, together with tests where the direction of change under the alternative is unspecified. Our tests retain the same rates of consistency against persistence change processes as their unmodified counterparts. Simulation evidence suggests that our new procedures work extremely well in practice, with the modified tests correctly being sized in both constant I(0) and constant I(1) environments, and displaying only very modest losses in power, relative to unmodified tests, against persistence change process

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 134 (2006)
Issue (Month): 2 (October)
Pages: 441-469

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Handle: RePEc:eee:econom:v:134:y:2006:i:2:p:441-469

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Web page: http://www.elsevier.com/locate/jeconom

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  1. Kim, Jae-Young & Belaire-Franch, Jorge & Amador, Rosa Badillo, 2002. "Corrigendum to "Detection of change in persistence of a linear time series" [J. Econom. 95 (2000) 97-116]," Journal of Econometrics, Elsevier, vol. 109(2), pages 389-392, August.
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  6. Peter C.B. Phillips & Pierre Perron, 1986. "Testing for a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 795R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
  7. Banerjee, Anindya & Lumsdaine, Robin L & Stock, James H, 1992. "Recursive and Sequential Tests of the Unit-Root and Trend-Break Hypotheses: Theory and International Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 271-87, July.
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  10. Stephen Leybourne & Tae-Hwan Kim & Vanessa Smith & Paul Newbold, 2003. "Tests for a change in persistence against the null of difference-stationarity," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 291-311, December.
  11. Kim, Jae-Young, 2000. "Detection of change in persistence of a linear time series," Journal of Econometrics, Elsevier, vol. 95(1), pages 97-116, March.
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  15. Busetti, Fabio & Taylor, A. M. Robert, 2004. "Tests of stationarity against a change in persistence," Journal of Econometrics, Elsevier, vol. 123(1), pages 33-66, November.
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