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

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

Contents:

Author Info

  • Giuseppe Cavaliere

    (Department of Statistical Sciences, University of Bologna)

  • Anders Rahbek

    (Department of Economics, University of Copenhagen)

  • A. M. Robert Taylor

    (University of Nottingham)

Abstract

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.

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.econ.ku.dk/english/research/publications/wp/2008/0834.pdf
Download Restriction: no

Bibliographic Info

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
Email:
Web page: http://www.econ.ku.dk
More information through EDIRC

Related research

Keywords: co-integration; non-stationary volatility; trace and maximum eigenvalue tests; wild bootstrap;

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. 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.
  2. 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.
  3. 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.
  4. John Y. Campbell & Robert J. Shiller, 1986. "Cointegration and Tests of Present Value Models," NBER Working Papers 1885, National Bureau of Economic Research, Inc.
  5. 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.
  6. Goncalves, Silvia & Kilian, Lutz, 2004. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 123(1), pages 89-120, November.
  7. Xu, Ke-Li & Phillips, Peter C.B., 2008. "Adaptive estimation of autoregressive models with time-varying variances," Journal of Econometrics, Elsevier, vol. 142(1), pages 265-280, January.
  8. Atsushi Inoue & Lutz Kilian, 2000. "Bootstrapping Autoregressive Processes with Possible Unit Roots," Econometric Society World Congress 2000 Contributed Papers 0401, Econometric Society.
  9. Margaret M. McConnell & Gabriel Perez Quiros, 1998. "Output fluctuations in the United States: what has changed since the early 1980s?," Staff Reports 41, Federal Reserve Bank of New York.
  10. 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.
  11. 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.
  12. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  13. 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.
  14. Loretan, Mico & Phillips, Peter C. B., 1994. "Testing the covariance stationarity of heavy-tailed time series: An overview of the theory with applications to several financial datasets," Journal of Empirical Finance, Elsevier, vol. 1(2), pages 211-248, January.
  15. Peter Reinhard Hansen, 2000. "Structural Changes in the Cointegrated Vector Autoregressive Model," Working Papers 2000-20, Brown University, Department of Economics.
  16. 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.
  17. 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.
  18. Johansen, S., 1991. "Determination of Cointegration Rank in the Presence of a Linear Trend," Papers 76a, Helsinki - Department of Economics.
  19. 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.
  20. 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.
  21. Giese, Julia V., 2008. "Level, Slope, Curvature: Characterising the Yield Curve in a Cointegrated VAR Model," Economics Discussion Papers 2008-13, Kiel Institute for the World Economy.
  22. Markku Lanne & Helmut Luetkepohl, 2005. "Structural Vector Autoregressions with Nonnormal Residuals," Economics Working Papers ECO2005/25, European University Institute.
  23. Boswijk, H.P., 2000. "Testing for a Unit Root with Near-Integrated Volatility," CeNDEF Working Papers 00-09, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  24. 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.
  25. Russell Davidson & Emmanuel Flachaire, 2000. "The Wild Bootstrap, Tamed at Last," Econometric Society World Congress 2000 Contributed Papers 1413, Econometric Society.
  26. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
  27. 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.
  28. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
  29. Bruce E. Hansen, 1998. "Testing for Structural Change in Conditional Models," Boston College Working Papers in Economics 310., Boston College Department of Economics.
  30. Hansen, Bruce E., 1992. "Heteroskedastic cointegration," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 139-158.
  31. 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.
  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. 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.
  34. Joon Y. Park, 2003. "Bootstrap Unit Root Tests," Econometrica, Econometric Society, vol. 71(6), pages 1845-1895, November.
  35. 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.
  36. 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.
  37. MacKinnon, James G & Haug, Alfred A & Michelis, Leo, 1999. "Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 563-77, Sept.-Oct.
  38. 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.
  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. 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.
  41. 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.
  42. Ke-Li Xu, 2008. "Bootstrapping Autoregression under Non-stationary Volatility," Econometrics Journal, Royal Economic Society, vol. 11(1), pages 1-26, 03.
  43. Efstathios Paparoditis & Dimitris N. Politis, 2003. "Residual-Based Block Bootstrap for Unit Root Testing," Econometrica, Econometric Society, vol. 71(3), pages 813-855, 05.
  44. 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.
  45. 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.
  46. Hansen, Bruce E, 1995. "Regression with Nonstationary Volatility," Econometrica, Econometric Society, vol. 63(5), pages 1113-32, September.
  47. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201.
  48. Giuseppe Cavaliere, 2005. "Unit Root Tests under Time-Varying Variances," Econometric Reviews, Taylor & Francis Journals, vol. 23(3), pages 259-292.
  49. 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.
  50. 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.
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:
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page.

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: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.