IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

Testing for Co-integration in Vector Autoregressions with Non-Stationary Volatility

  • Giuseppe Cavaliere

    (Department of Statistical Sciences, University of Bologna)

  • Anders Rahbek

    (Department of Economics, University of Copenhagen)

  • A. M. Robert Taylor

    (University of Nottingham)

Many key macro-economic and ?nancial variables are characterised by permanent changes in unconditional volatility. In this paper we analyse vector autoregressions with non-stationary (unconditional) volatility of a very general form, which includes single and multiple volatility breaks as special cases. We show that the conventional rank statistics computed as in Johansen (1988,1991) are potentially unreliable. In particular, their large sample distributions depend on the integrated covariation of the underlying multivariate volatility process which impacts on both the size and power of the associated co-integration tests, as we demonstrate numerically. A solution to the identi?ed inference problem is provided by considering wild bootstrap-based implementations of the rank tests. These do not require the practitioner to specify a parametric model for volatility, nor to assume that the pattern of volatility is common to, or independent across, the vector of series under analysis. The bootstrap is shown to perform very 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://www.econ.ku.dk/english/research/publications/wp/2008/0834.pdf
Download Restriction: no

Paper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 08-34.

as
in new window

Length: 28 pages
Date of creation: Sep 2008
Date of revision:
Handle: RePEc:kud:kuiedp:0834
Contact details of provider: Postal:
Øster Farimagsgade 5, Building 26, DK-1353 Copenhagen K., Denmark

Phone: (+45) 35 32 30 10
Fax: +45 35 32 30 00
Web page: http://www.econ.ku.dk
Email:


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. Russell Davidson & Emmanuel Flachaire, 2001. "The Wild Bootstrap, Tamed at Last," Working Papers 1000, Queen's University, Department of Economics.
  2. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201, December.
  3. Park, Joon, 2002. "Bootstrap Unit Root Tests," Working Papers 2003-04, Rice University, Department of Economics.
  4. Cheung, Yin-Wong & Lai, Kon S, 1993. "Finite-Sample Sizes of Johansen's Likelihood Ration Tests for Conintegration," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 55(3), pages 313-28, August.
  5. Atsushi Inoue & Lutz Kilian, 2000. "Bootstrapping Autoregressive Processes with Possible Unit Roots," Econometric Society World Congress 2000 Contributed Papers 0401, Econometric Society.
  6. Bruce E. Hansen, 1998. "Testing for Structural Change in Conditional Models," Boston College Working Papers in Economics 310., Boston College Department of Economics.
  7. Campbell, John Y & Shiller, Robert J, 1987. "Cointegration and Tests of Present Value Models," Journal of Political Economy, University of Chicago Press, vol. 95(5), pages 1062-88, October.
  8. Markku Lanne & Helmut Luetkepohl, 2005. "Structural Vector Autoregressions with Nonnormal Residuals," Economics Working Papers ECO2005/25, European University Institute.
  9. Giuseppe Cavaliere & A. M. Robert Taylor, 2006. "Testing the Null of Co-integration in the Presence of Variance Breaks," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(4), pages 613-636, 07.
  10. 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.
  11. Bruce E. Hansen, 1996. "Sample Splitting and Threshold Estimation," Boston College Working Papers in Economics 319., Boston College Department of Economics, revised 12 May 1998.
  12. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
  13. James A. Kahn & Margaret M. McConnell & Gabriel Perez-Quiros, 2002. "On the causes of the increased stability of the U.S. economy," Economic Policy Review, Federal Reserve Bank of New York, issue May, pages 183-202.
  14. Giese, Julia V., 2008. "Level, Slope, Curvature: Characterising the Yield Curve in a Cointegrated VAR Model," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy (IfW), vol. 2, pages 1-20.
  15. Hansen, Peter Reinhard, 2003. "Structural changes in the cointegrated vector autoregressive model," Journal of Econometrics, Elsevier, vol. 114(2), pages 261-295, June.
  16. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  17. Marianne Sensier & Dick van Dijk, 2004. "Testing for Volatility Changes in U.S. Macroeconomic Time Series," The Review of Economics and Statistics, MIT Press, vol. 86(3), pages 833-839, August.
  18. Lanne, Markku & Saikkonen, Pentti, 2007. "A Multivariate Generalized Orthogonal Factor GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 61-75, January.
  19. Roy van der Weide, 2002. "GO-GARCH: a multivariate generalized orthogonal GARCH model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 549-564.
  20. Anders Rygh Swensen, 2006. "Bootstrap Algorithms for Testing and Determining the Cointegration Rank in VAR Models -super-1," Econometrica, Econometric Society, vol. 74(6), pages 1699-1714, November.
  21. Giuseppe Cavaliere, 2003. "Unit root tests under time-varying variances," Quaderni di Dipartimento 2, Department of Statistics, University of Bologna.
  22. Hansen, Bruce E., 1992. "Heteroskedastic cointegration," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 139-158.
  23. Mackinnon, J.G. & Haug, A.A. & Michelis, L., 1996. "Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration," G.R.E.Q.A.M. 96a09, Universite Aix-Marseille III.
  24. Peter C. B. Phillips & Ke-Li Xu, 2006. "Inference in Autoregression under Heteroskedasticity," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(2), pages 289-308, 03.
  25. Margaret M. McConnell & Gabriel Perez-Quiros, 2000. "Output fluctuations in the United States: what has changed since the early 1980s?," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
  26. Mark W. Watson, 1999. "Explaining the increased variability in long-term interest rates," Economic Quarterly, Federal Reserve Bank of Richmond, issue Fall, pages 71-96.
  27. Burridge, Peter & Taylor, A. M. Robert, 2001. "On regression-based tests for seasonal unit roots in the presence of periodic heteroscedasticity," Journal of Econometrics, Elsevier, vol. 104(1), pages 91-117, August.
  28. van Dijk, D.J.C. & Osborn, D.R. & Sensier, M., 2002. "Changes in variability of the business cycle in the G7 countries," Econometric Institute Research Papers EI 2002-28, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  29. Ke-Li Xu & Peter C.B. Phillips, 2006. "Adaptive Estimation of Autoregressive Models with Time-Varying Variances," Cowles Foundation Discussion Papers 1585R, Cowles Foundation for Research in Economics, Yale University, revised Nov 2006.
  30. 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.
  31. Loretan, M. & Phillips, P.C.B., 1992. "Testing the Covariance Stationarity of Heavy-Tailed Time Series: An Overview of the Theory with Applications to Several Financial Datasets," Working papers 9208, Wisconsin Madison - Social Systems.
  32. Osterwald-Lenum, Michael, 1992. "A Note with Quantiles of the Asymptotic Distribution of the Maximum Likelihood Cointegration Rank Test Statistics," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 461-72, August.
  33. Soren Johansen, 2002. "A Small Sample Correction for the Test of Cointegrating Rank in the Vector Autoregressive Model," Econometrica, Econometric Society, vol. 70(5), pages 1929-1961, September.
  34. Chang-Jin Kim & Charles R. Nelson, 1999. "Has The U.S. Economy Become More Stable? A Bayesian Approach Based On A Markov-Switching Model Of The Business Cycle," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 608-616, November.
  35. 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.
  36. Seo, Byeongseon, 2007. "Asymptotic distribution of the cointegrating vector estimator in error correction models with conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 137(1), pages 68-111, March.
  37. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November.
  38. 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).
  39. Hall, Anthony D & Anderson, Heather M & Granger, Clive W J, 1992. "A Cointegration Analysis of Treasury Bill Yields," The Review of Economics and Statistics, MIT Press, vol. 74(1), pages 116-26, February.
  40. 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.
  41. Johansen, S., 1991. "Determination of Cointegration Rank in the Presence of a Linear Trend," Papers 76a, Helsinki - Department of Economics.
  42. Ke-Li Xu, 2008. "Bootstrapping Autoregression under Non-stationary Volatility," Econometrics Journal, Royal Economic Society, vol. 11(1), pages 1-26, 03.
  43. Hansen, Bruce E, 1995. "Regression with Nonstationary Volatility," Econometrica, Econometric Society, vol. 63(5), pages 1113-32, September.
  44. Giuseppe Cavaliere & A. M. Robert Taylor, 2008. "Time-Transformed Unit Root Tests for Models with Non-Stationary Volatility," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(2), pages 300-330, 03.
  45. 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.
  46. Hamori, Shigeyuki & Tokihisa, Akira, 1997. "Testing for a unit root in the presence of a variance shift1," Economics Letters, Elsevier, vol. 57(3), pages 245-253, December.
  47. Donald W. K. Andrews & Moshe Buchinsky, 2000. "A Three-Step Method for Choosing the Number of Bootstrap Repetitions," Econometrica, Econometric Society, vol. 68(1), pages 23-52, January.
  48. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
  49. 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:kud:kuiedp:0834. 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: (Thomas Hoffmann)

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.