IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Testing for unit roots in the presence of a possible break in trend and non-stationary volatility

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

In this paper we analyse the impact of non-stationary volatility on the recently developed unit root tests which allow for a possible break in trend occurring at an unknown point in the sample, considered in Harris, Harvey, Leybourne and Taylor (2009) [HHLT]. HHLT's analysis hinges on a new break fraction estimator which, when a break in trend occurs, is consistent for the true break fraction at rate Op(T^-1). Unlike other available estimators, however, when there is no trend break HHLT's estimator converges to zero at rate Op(T^-1/2). In their analysis HHLT assume the shocks to follow a linear process driven by IID innovations. Our first contribution is to show that HHLT's break fraction estimator retains the same consistency properties as demonstrated by HHLT for the IID case when the innovations display non-stationary behaviour of a quite general form, including, for example, the case of a single break in the volatility of the innovations which may or may not occur at the same time as a break in trend. However, as we subsequently demonstrate, the limiting null distribution of unit root statistics based around this estimator are not pivotal in the presence of non-stationary volatility. Associated Monte Carlo evidence is presented to quantify the impact of a one-time change in volatility on both the asymptotic and finite sample behaviour of such tests. A solution to the identified inference problem is then provided by considering wild bootstrap-based implementations of the HHLT tests, using the trend break estimator from the original sample data. The proposed bootstrap method does not require the practitioner to specify a parametric model for volatility, and is shown to perform very well in practice across a range of models.

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/09-05.pdf
Download Restriction: no

Paper provided by University of Nottingham, Granger Centre for Time Series Econometrics in its series Discussion Papers with number 09/05.

as
in new window

Length:
Date of creation: Dec 2009
Date of revision:
Handle: RePEc:not:notgts:09/05
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

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. Kim, Dukpa & Perron, Pierre, 2009. "Unit root tests allowing for a break in the trend function at an unknown time under both the null and alternative hypotheses," Journal of Econometrics, Elsevier, vol. 148(1), pages 1-13, January.
  2. Nunes, Luis C. & Kuan, Chung-Ming & Newbold, Paul, 1995. "Spurious Break," Econometric Theory, Cambridge University Press, vol. 11(04), pages 736-749, August.
  3. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2008. "Bootstrap Unit Root Tests For Time Series With Nonstationary Volatility," Econometric Theory, Cambridge University Press, vol. 24(01), pages 43-71, February.
  4. Davidson, R. & Flachaire, E., 1999. "The Wild Bootstrap, Tamed at Last," G.R.E.Q.A.M. 99a32, Universite Aix-Marseille III.
  5. GONÇALVES, Silvia & KILIAN, Lutz, 2003. "Bootstrapping Autoregressions with Conditional Heteroskedasticity of Unknown Form," Cahiers de recherche 2003-01, Universite de Montreal, Departement de sciences economiques.
  6. Perron, Pierre & Rodriguez, Gabriel, 2003. "GLS detrending, efficient unit root tests and structural change," Journal of Econometrics, Elsevier, vol. 115(1), pages 1-27, July.
  7. Vogelsang, T.J. & Perron, P., 1994. "Additional Tests for a Unit Root Allowing for a Break in the Trend Function at an Unknown Time," Cahiers de recherche 9422, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  8. Perron, P., 1994. "Further Evidence on Breaking Trend Functions in Macroeconomic Variables," Cahiers de recherche 9421, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  9. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
  10. Christiano, Lawrence J, 1992. "Searching for a Break in GNP," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 237-50, July.
  11. Perron, P. & Ng, S., 1994. "Useful Modifications to Some Unit Root Tests with Dependent Errors and Their Local Asymptotic Properties," Cahiers de recherche 9427, Universite de Montreal, Departement de sciences economiques.
  12. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2007. "Testing for unit roots in time series models with non-stationary volatility," Journal of Econometrics, Elsevier, vol. 140(2), pages 919-947, October.
  13. Hansen, B.E., 1991. "Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis," RCER Working Papers 296, University of Rochester - Center for Economic Research (RCER).
  14. repec:bot:quadip:89 is not listed on IDEAS
  15. Fabio Busetti & Andrew Harvey, 2007. "Testing for trend," Temi di discussione (Economic working papers) 614, Bank of Italy, Economic Research and International Relations Area.
  16. Kim, Tae-Hwan & Leybourne, Stephen & Newbold, Paul, 2002. "Unit root tests with a break in innovation variance," Journal of Econometrics, Elsevier, vol. 109(2), pages 365-387, August.
  17. Yoosoon Chang & Joon Y. Park, 2003. "A Sieve Bootstrap For The Test Of A Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 379-400, 07.
  18. 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.
  19. 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.
  20. Andrews, Donald W. K. & Buchinsky, Moshe, 2001. "Evaluation of a three-step method for choosing the number of bootstrap repetitions," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 345-386, July.
  21. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-36, July.
  22. repec:cup:etheor:v:24:y:2007:i:01:p:43-71 is not listed on IDEAS
  23. Perron, Pierre & Zhu, Xiaokang, 2005. "Structural breaks with deterministic and stochastic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 65-119.
  24. 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.
  25. repec:cup:etheor:v:24:y:2007:i:01:p:43-71_08 is not listed on IDEAS
  26. 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.
  27. David Harris & David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2007. "Testing for a unit root in the presence of a possible break in trend," Discussion Papers 07/04, University of Nottingham, Granger Centre for Time Series Econometrics.
  28. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
  29. M Sensier & D van Dijk, 2003. "Testing for Volatility Changes in US Macroeconomic Time Series," Centre for Growth and Business Cycle Research Discussion Paper Series 36, Economics, The Univeristy of Manchester.
  30. Silvia Goncalves & Lutz Kilian, 2007. "Asymptotic and Bootstrap Inference for AR(∞) Processes with Conditional Heteroskedasticity," Econometric Reviews, Taylor & Francis Journals, vol. 26(6), pages 609-641.
  31. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2005. "Stationarity Tests Under Time-Varying Second Moments," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1112-1129, December.
  32. Efstathios Paparoditis & Dimitris N. Politis, 2003. "Residual-Based Block Bootstrap for Unit Root Testing," Econometrica, Econometric Society, vol. 71(3), pages 813-855, 05.
Full references (including those not matched with items on IDEAS)

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

When requesting a correction, please mention this item's handle: RePEc:not:notgts:09/05. 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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.