Advanced Search
MyIDEAS: Login to save this paper or follow this series

Unit root testing under a local break in trend

Contents:

Author Info

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

Abstract

It is well known that it is vital to account for trend breaks when testing for a unit root. In practice, uncertainty exists over whether or not a trend break is present and, if it is, where it is located. Harris et al. (2009) and Carrion-i-Silvestre et al. (2009) propose procedures which account for both of these forms of uncertainty. Each uses what amounts to a pre-test for a trend break, accounting for a trend break (the associated break fraction estimated from the data) in the unit root procedure only where the pre-test signals a break. Assuming the break magnitude is fixed (independent of sample size) these authors show that their methods achieve near asymptotically ecient unit root inference in both trend break and no trend break environments. These asymptotic results are, however, somewhat at odds with the finite sample simulations reported in both papers. These show the presence of pronounced "valleys" in the finite sample power functions (when mapped as functions of the break magnitude) of the tests such that power is initially high for very small breaks, then decreases as the break magnitude increases, before increasing again. Here we show that treating the break magnitude as local to zero (in a Pitman drift sense) allows the asymptotic analysis to very closely approximate this finite sample effect, thereby providing useful analytical insights into the observed phenomenon. In response to this problem we propose practical solutions, based either on the use of a with break unit root test but with adaptive critical values, or on a union of rejections principle taken across with break and without break unit root tests. The former is shown to eliminate power valleys but at the expense of power when no break is present, while the latter considerably mitigates the valleys while not losing all the power gains available when no break exists.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.nottingham.ac.uk/economics/grangercentre/papers/11-02.pdf
Download Restriction: no

Bibliographic Info

Paper provided by University of Nottingham, Granger Centre for Time Series Econometrics in its series Discussion Papers with number 10/05.

as in new window
Length:
Date of creation: Sep 2010
Date of revision:
Handle: RePEc:not:notgts:10/05

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/
More information through EDIRC

Related research

Keywords: Unit root test; local trend break; asymptotic local power; union of rejections; adaptive critical values;

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Pierre Perron & Tomoyoshi Yabu, 2007. "Estimating Deterministic Trend with an Integrated or Stationary Noise Component," Boston University - Department of Economics - Working Papers Series WP2007-020, Boston University - Department of Economics.
  2. Pierre Perron & Tomoyoshi Yabu, 2005. "Testing for Shifts in Trend with an Integrated or Stationary Noise Component," Boston University - Department of Economics - Working Papers Series WP2005-026, Boston University - Department of Economics.
  3. Josep Lluís Carrion-i-Silvestre & Dukpa Kim & Pierre Perron, 2007. "GLS-based unit root tests with multiple structural breaks both under the null and the alternative hypotheses," Boston University - Department of Economics - Working Papers Series wp2008-019, Boston University - Department of Economics.
  4. 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.
  5. Perron, Pierre & Qu, Zhongjun, 2007. "A simple modification to improve the finite sample properties of Ng and Perron's unit root tests," Economics Letters, Elsevier, vol. 94(1), pages 12-19, January.
  6. James H. Stock & Mark W. Watson, 1994. "Evidence on Structural Instability in Macroeconomic Time Series Relations," NBER Technical Working Papers 0164, National Bureau of Economic Research, Inc.
  7. Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "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?," Cowles Foundation Discussion Papers 979, Cowles Foundation for Research in Economics, Yale University.
  8. 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.
  9. Perron, P., 1990. "Further Evidence On Breaking Trend Functions In Macroeconomics Variables," Papers 350, Princeton, Department of Economics - Econometric Research Program.
  10. Mohitosh Kejriwal & Pierre Perron, 2009. "A Sequential Procedure to Determine the Number of Breaks in Trend with an Integrated or Stationary Noise Component," Purdue University Economics Working Papers 1217, Purdue University, Department of Economics.
  11. 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.
  12. Mohitosh Kejriwal & Pierre Perron, 2006. "Unit Root Tests Allowing for a Break in the Trend Function at an Unknown Time Under Both the Null and Alternative Hypotheses," Boston University - Department of Economics - Working Papers Series WP2006-052, Boston University - Department of Economics.
  13. Jingjing Yang, 2012. "Break point estimators for a slope shift: levels versus first differences," Econometrics Journal, Royal Economic Society, vol. 15(1), pages 154-169, 02.
  14. Eric Zivot & Donald W.K. Andrews, 1990. "Further Evidence on the Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Cowles Foundation Discussion Papers 944, Cowles Foundation for Research in Economics, Yale University.
  15. PERRON, Pierre & RODRIGUEZ, Gabriel, 1998. "GLS Detrending, Efficient Unit Root Tests and Structural Change," Cahiers de recherche 9809, Universite de Montreal, Departement de sciences economiques.
  16. 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.
  17. Carrion-i-Silvestre, Josep Lluís & Kim, Dukpa & Perron, Pierre, 2009. "Gls-Based Unit Root Tests With Multiple Structural Breaks Under Both The Null And The Alternative Hypotheses," Econometric Theory, Cambridge University Press, vol. 25(06), pages 1754-1792, December.
  18. David I. Harvey & Stephen J. Leybourne & A.M. Robert Taylor, . "Simple, Robust and Powerful Tests of the Breaking Trend Hypothesis," Discussion Papers 06/11, University of Nottingham, School of Economics.
  19. Vogelsang, Timothy J., 1997. "Wald-Type Tests for Detecting Breaks in the Trend Function of a Dynamic Time Series," Econometric Theory, Cambridge University Press, vol. 13(06), pages 818-848, December.
  20. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
  21. 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.
  22. 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.
  23. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
  24. James H. Stock & Mark W. Watson, 2005. "Implications of Dynamic Factor Models for VAR Analysis," NBER Working Papers 11467, National Bureau of Economic Research, Inc.
  25. Perron, Pierre & Zhu, Xiaokang, 2005. "Structural breaks with deterministic and stochastic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 65-119.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2013. "Testing for unit roots in the possible presence of multiple trend breaks using minimum Dickey–Fuller statistics," Journal of Econometrics, Elsevier, vol. 177(2), pages 265-284.
  2. Anton Skrobotov, 2014. "On Trend, Breaks and Initial Condition in Unit Root Testing," Working Papers 0097, Gaidar Institute for Economic Policy, revised 2014.
  3. Anton Skrobotov, 2013. "Local Structural Trend Break in Stationarity Testing," Working Papers 0074, Gaidar Institute for Economic Policy, revised 2013.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:not:notgts:10/05. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ().

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.