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Testing for a unit root when uncertain about the trend [Revised to become 07/03 above]

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

Abstract

In this paper we consider the issue of testing for a unit root when it is uncertain as to whether or not a linear deterministic trend is present in the data. The Dickey-Fuller-type tests of Elliott, Rothenberg and Stock (1996), based on (local) GLS detrended (demeaned) data, are near asymptotically efficient when a deterministic trend is (is not) present in the data generating process. We consider a variety of strategies which aim to select the demeaned variant when a trend is not present and the detrended variant otherwise. Asymptotic and finite sample evidence demonstrates that some sophisticated strategies which involve auxiliary methods of trend detection are generally outperformed by a simple decision rule of rejecting the unit root null whenever either the GLS demeaned or GLS detrended Dickey-Fuller-type tests reject. We show that this simple strategy is asymptotically identical to a sequential testing strategy proposed by Ayat and Burridge (2000). Moreover, our results make it clear that any other unit root testing strategy, however elaborate, can at best only offer a rather modest improvement over the simple one.

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File URL: http://www.nottingham.ac.uk/economics/grangercentre/papers/07-03.pdf
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Bibliographic Info

Paper provided by University of Nottingham, Granger Centre for Time Series Econometrics in its series Discussion Papers with number 06/03.

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Date of creation: Oct 2007
Date of revision:
Handle: RePEc:not:notgts:06/03

Contact details of provider:
Postal: School of Economics University of Nottingham University Park Nottingham NG7 2RD
Phone: (44) 0115 951 5620
Fax: (0115) 951 4159
Web page: http://www.nottingham.ac.uk/economics/grangercentre/
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Related research

Keywords: Unit root test; trend uncertainty; initial condition; asymtotic power; union of rejections decision rule;

References

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  1. David I. Harvey, & Stephen J. Leybourne, & A. M. Robert Taylor, 2006. "A simple, robust and powerful test of the trend hypothesis," Discussion Papers 06/01, University of Nottingham, Granger Centre for Time Series Econometrics.
  2. Harris, David & Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Testing For A Unit Root In The Presence Of A Possible Break In Trend," Econometric Theory, Cambridge University Press, vol. 25(06), pages 1545-1588, December.
  3. Peter C.B. Phillips & Werner Ploberger, 1992. "Posterior Odds Testing for a Unit Root with Data-Based Model Selection," Cowles Foundation Discussion Papers 1017, Cowles Foundation for Research in Economics, Yale University.
  4. Ayat, L. & Burridge, P., 1996. "Unit Root Tests in the presence of Uncertainty about the Non-Stochastic Trends," Discussion Papers 96-28, Department of Economics, University of Birmingham.
  5. 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.
  6. Schmidt, Peter & Phillips, C B Peter, 1992. "LM Tests for a Unit Root in the Presence of Deterministic Trends," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 257-87, August.
  7. Marsh, Patrick, 2007. "The Available Information For Invariant Tests Of A Unit Root," Econometric Theory, Cambridge University Press, vol. 23(04), pages 686-710, August.
  8. Zhije Xiao & Peter C.B. Phillips, 1998. "An ADF coefficient test for a unit root in ARMA models of unknown order with empirical applications to the US economy," Econometrics Journal, Royal Economic Society, vol. 1(RegularPa), pages 27-43.
  9. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  10. Yoosoon Chang & Joon Park, 2002. "On The Asymptotics Of Adf Tests For Unit Roots," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 431-447.
  11. 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.
  12. Elliott, Graham, 1999. "Efficient Tests for a Unit Root When the Initial Observation Is Drawn from Its Unconditional Distribution," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(3), pages 767-83, August.
  13. 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 10353, Iowa State University, Department of Economics.
  14. Newey, Whitney K & West, Kenneth D, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," Review of Economic Studies, Wiley Blackwell, vol. 61(4), pages 631-53, October.
  15. Ulrich K. M¸ller & Graham Elliott, 2003. "Tests for Unit Roots and the Initial Condition," Econometrica, Econometric Society, vol. 71(4), pages 1269-1286, 07.
  16. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
  17. Phillips, P C B, 1991. "To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 333-64, Oct.-Dec..
  18. Peter C.B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Cowles Foundation Discussion Papers 1189, Cowles Foundation for Research in Economics, Yale University.
  19. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
  20. West, Kenneth D, 1988. "Asymptotic Normality, When Regressors Have a Unit Root," Econometrica, Econometric Society, vol. 56(6), pages 1397-1417, November.
  21. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
  22. Elliott, Graham & Muller, Ulrich K., 2006. "Minimizing the impact of the initial condition on testing for unit roots," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 285-310.
  23. Michael Jansson, 2007. "Semiparametric Power Envelopes for Tests of the Unit Root Hypothesis," CREATES Research Papers 2007-12, School of Economics and Management, University of Aarhus.
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