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

Testing For Unit Roots In The Presence Of A Possible Break In Trend And Nonstationary Volatility

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

We analyze the impact of nonstationary volatility on the break fraction estimator and associated trend break unit root tests of Harris, Harvey, Leybourne, and Taylor (2009) (HHLT). We show that although HHLT’s break fraction estimator retains the same large-sample properties as demonstrated by HHLT for homoskedastic shocks, the limiting null distributions of unit root statistics based around this estimator are not pivotal under nonstationary volatility. A solution to the identified inference problem, which does not require the practitioner to specify a parametric model for volatility, is provided using the wild bootstrap and is shown to perform well in practice.

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://journals.cambridge.org/abstract_S0266466610000605
File Function: link to article abstract page
Download Restriction: no

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 27 (2011)
Issue (Month): 05 (October)
Pages: 957-991

as
in new window

Handle: RePEc:cup:etheor:v:27:y:2011:i:05:p:957-991_00
Contact details of provider: Postal: Cambridge University Press, UPH, Shaftesbury Road, Cambridge CB2 8BS UK
Web page: http://journals.cambridge.org/jid_ECTEmail:

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. 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.
  2. 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.
  3. 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.
  4. James H. Stock & Mark W. Watson, 1994. "Evidence on structural instability in macroeconomic times series relations," Working Paper Series, Macroeconomic Issues 94-13, Federal Reserve Bank of Chicago.
  5. 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.
  6. Russell Davidson & Emmanuel Flachaire, 2000. "The Wild Bootstrap, Tamed at Last," Econometric Society World Congress 2000 Contributed Papers 1413, Econometric Society.
  7. Giuseppe Cavaliere, 2005. "Unit Root Tests under Time-Varying Variances," Econometric Reviews, Taylor & Francis Journals, vol. 23(3), pages 259-292.
  8. Perron, P., 1990. "Further Evidence On Breaking Trend Functions In Macroeconomics Variables," Papers 350, Princeton, Department of Economics - Econometric Research Program.
  9. 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.
  10. Perron, Pierre & Ng, Serena, 1996. "Useful Modifications to Some Unit Root Tests with Dependent Errors and Their Local Asymptotic Properties," Review of Economic Studies, Wiley Blackwell, vol. 63(3), pages 435-63, July.
  11. 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.
  12. Kilian, Lutz & Gonçalves, Sílvia, 2002. "Bootstrapping Autoregressions with Conditional Heteroskedasticity of Unknown Form," Discussion Paper Series 1: Economic Studies 2002,26, Deutsche Bundesbank, Research Centre.
  13. repec:cup:etheor:v:24:y:2007:i:01:p:43-71 is not listed on IDEAS
  14. Serena Ng & Pierre Perron, 1997. "Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power," Boston College Working Papers in Economics 369, Boston College Department of Economics, revised 01 Sep 2000.
  15. 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.
  16. repec:cup:etheor:v:24:y:2007:i:01:p:43-71_08 is not listed on IDEAS
  17. 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.
  18. 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.
  19. Efstathios Paparoditis & Dimitris N. Politis, 2003. "Residual-Based Block Bootstrap for Unit Root Testing," Econometrica, Econometric Society, vol. 71(3), pages 813-855, 05.
  20. 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.
  21. 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.
  22. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-30, March.
  23. 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.
  24. Nunes, Luis C. & Kuan, Chung-Ming & Newbold, Paul, 1995. "Spurious Break," Econometric Theory, Cambridge University Press, vol. 11(04), pages 736-749, August.
  25. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
  26. 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.
  27. 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.
  28. Perron, Pierre & Zhu, Xiaokang, 2005. "Structural breaks with deterministic and stochastic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 65-119.
  29. 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.
  30. 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.
  31. 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.
  32. Fabio Busetti & Andrew Harvey, 2007. "Testing for trend," Temi di discussione (Economic working papers) 614, Bank of Italy, Economic Research and International Relations Area.
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:cup:etheor:v:27:y:2011:i:05:p:957-991_00. 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: (Keith Waters)

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.