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Modified Tests for a Change in Persistence

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  • Robert Taylor
  • Stephen Leybourne
  • David Harvey

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

Paper provided by Econometric Society in its series Econometric Society 2004 Australasian Meetings with number 64.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:ausm04:64

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Keywords: trend stationary; difference stationary; persistence change;

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References

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  1. Robert G. King & Charles I. Plosser & James H. Stock & Mark W. Watson, 1992. "Stochastic Trends and Economic Fluctuations," NBER Working Papers 2229, National Bureau of Economic Research, Inc.
  2. Anindya Banerjee & Robin L. Lumsdaine & James H. Stock, 1990. "Recursive and Sequential Tests of the Unit Root and Trend Break Hypothesis: Theory and International Evidence," NBER Working Papers 3510, National Bureau of Economic Research, Inc.
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  4. Richard Clarida & Jordi Galí & Mark Gertler, 2000. "Monetary Policy Rules And Macroeconomic Stability: Evidence And Some Theory," The Quarterly Journal of Economics, MIT Press, vol. 115(1), pages 147-180, February.
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  7. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
  8. 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.
  9. 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.
  10. Peter C. B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-470, December.
  11. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
  12. 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.
  13. Emery, Kenneth M., 1994. "Inflation persistence and Fisher effects: Evidence of a regime change," Journal of Economics and Business, Elsevier, vol. 46(3), pages 141-152, August.
  14. 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.
  15. Vogelsang, Timothy J, 1998. "Testing for a Shift in Mean without Having to Estimate Serial-Correlation Parameters," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(1), pages 73-80, January.
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