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The impact of the initial condition on robust tests for a linear trend

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

Abstract

This article examines the behaviour of some recently proposed 'robust' (to the order of integration of the data) tests for the presence of a deterministic linear trend in a univariate times series in situations where the magnitude of the initial condition of the series is non-negligible. We demonstrate that the asymptotic size and/or local power properties of these tests are extremely sensitive to the initial condition. Straightforward modifications to the trend tests are suggested, based on the use of trimmed data, which are shown to help reduce this sensitivity. Copyright Copyright 2010 Blackwell Publishing Ltd

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Bibliographic Info

Article provided by Wiley Blackwell in its journal Journal of Time Series Analysis.

Volume (Year): 31 (2010)
Issue (Month): 4 (07)
Pages: 292-302

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Handle: RePEc:bla:jtsera:v:31:y:2010:i:4:p:292-302

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Web page: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782

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  1. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2007. "A simple, robust and powerful test of the trend hypothesis," Journal of Econometrics, Elsevier, Elsevier, vol. 141(2), pages 1302-1330, December.
  2. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Unit Root Testing In Practice: Dealing With Uncertainty Over The Trend And Initial Condition," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 25(03), pages 587-636, June.
  3. Pierre Perron & Tomoyoshi Yabu, 2007. "Estimating Deterministic Trend with an Integrated or Stationary Noise Component," Boston University - Department of Economics - Working Papers Series, Boston University - Department of Economics WP2007-020, Boston University - Department of Economics.
  4. Bunzel, Helle & Vogelsang, Timothy J., 2003. "Powerful Trend Function Tests That Are Robust to Strong Serial Correlation with an Application to the Prebisch-Singer Hypothesis," Staff General Research Papers, Iowa State University, Department of Economics 10353, Iowa State University, Department of Economics.
  5. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 21(06), pages 1130-1164, December.
  6. Graham Elliott & Thomas J. Rothenberg & James H. Stock, 1992. "Efficient Tests for an Autoregressive Unit Root," NBER Technical Working Papers 0130, National Bureau of Economic Research, Inc.
  7. Kwiatkowski, D. & Phillips, P.C.B. & Schmidt, P., 1990. "Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root : How Sure are we that Economic Time Series have a Unit Root?," Papers, Michigan State - Econometrics and Economic Theory 8905, Michigan State - Econometrics and Economic Theory.
  8. Elliott, Graham & Muller, Ulrich K., 2006. "Minimizing the impact of the initial condition on testing for unit roots," Journal of Econometrics, Elsevier, Elsevier, vol. 135(1-2), pages 285-310.
  9. David I. Harvey & Stephen J. Leybourne, 2005. "On testing for unit roots and the initial observation," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 8(1), pages 97-111, 03.
  10. Ulrich K. M¸ller & Graham Elliott, 2003. "Tests for Unit Roots and the Initial Condition," Econometrica, Econometric Society, Econometric Society, vol. 71(4), pages 1269-1286, 07.
  11. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, Econometric Society, vol. 66(1), pages 123-148, January.
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Cited by:
  1. Anton Skrobotov, 2012. "Trend and initial condition in stationarity tests: the asymptotic analysis," Working Papers, Gaidar Institute for Economic Policy 0048, Gaidar Institute for Economic Policy, revised 2013.
  2. Terence Mills, 2013. "Breaks and unit roots in global and hemispheric temperatures: an updated analysis," Climatic Change, Springer, Springer, vol. 118(3), pages 745-755, June.

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