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Bootstrap Sequential Determination of the Co-integration Rank in VAR Models

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Author Info

  • Guiseppe Cavaliere

    ()
    (Department of Statistical Sciences, University of Bologna)

  • Anders Rahbek

    ()
    (Department of Economics, University of Copenhagen and CREATES)

  • A.M.Robert Taylor

    ()
    (School of Economics and Granger Centre for Time Series Econometrics, University of Nottingham)

Abstract

Determining the co-integrating rank of a system of variables has become a fundamental aspect of applied research in macroeconomics and finance. It is wellknown that standard asymptotic likelihood ratio tests for co-integration rank of Johansen (1996) can be unreliable in small samples with empirical rejection frequencies often very much in excess of the nominal level. As a consequence, bootstrap versions of these tests have been developed. To be useful, however, sequential procedures for determining the co-integrating rank based on these bootstrap tests need to be consistent, in the sense that the probability of selecting a rank smaller than (equal to) the true co-integrating rank will converge to zero (one minus the marginal significance level), as the sample size diverges, for general I(1) processes. No such likelihood-based procedure is currently known to be available. In this paper we fill this gap in the literature by proposing a bootstrap sequential algorithm which we demonstrate delivers consistent cointegration rank estimation for general I(1) processes. Finite sample Monte Carlo simulations show the proposed procedure performs well in practice.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2010-07.

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Length: 23
Date of creation: 01 Feb 2010
Date of revision:
Handle: RePEc:aah:create:2010-07

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: Co-integration; trace test; sequential rank determination; i.i.d.bootstrap; wild bootstrap;

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References

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  1. Gonçalves, Sílvia & Kilian, Lutz, 2002. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Working Paper Series 0196, European Central Bank.
  2. 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.
  3. 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).
  4. Giuseppe Cavaliere & Anders Rahbek & A. M. Robert Taylor, 2008. "Testing for Co-integration in Vector Autoregressions with Non-Stationary Volatility," Discussion Papers 08-34, University of Copenhagen. Department of Economics.
  5. Paruolo, Paolo, 2001. " The Power of Lambda Max," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 63(3), pages 395-403, July.
  6. van Giersbergen, Noud P A, 1996. "Bootstrapping the Trace Statistic in VAR Models: Monte Carlo Results and Applications," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(2), pages 391-408, May.
  7. Trenkler, Carsten, 2009. "Bootstrapping Systems Cointegration Tests With A Prior Adjustment For Deterministic Terms," Econometric Theory, Cambridge University Press, vol. 25(01), pages 243-269, February.
  8. Anders Rygh Swensen, 2009. "Corrigendum to "Bootstrap Algorithms for Testing and Determining the Cointegration Rank in VAR Models"," Econometrica, Econometric Society, vol. 77(5), pages 1703-1704, 09.
  9. Giuseppe Cavaliere & Anders Rahbek & A.M.Robert Taylor, 2009. "Co-integration Rank Testing under Conditional Heteroskedasticity," CREATES Research Papers 2009-22, School of Economics and Management, University of Aarhus.
  10. Harris, R. I. D. & Judge, G., 1998. "Small sample testing for cointegration using the bootstrap approach," Economics Letters, Elsevier, vol. 58(1), pages 31-37, January.
  11. Nielsen, Bent & Rahbek, Anders, 2000. " Similarity Issues in Cointegration Analysis," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 62(1), pages 5-22, February.
  12. 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.
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Citations

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Cited by:
  1. Bicu Andreea & Candelon Bertrand, 2012. "Government bond market dynamics and sovereign risk: systemic or idiosyncratic?," Research Memorandum 032, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. Cavaliere, Giuseppe & Taylor, A. M. Robert & Trenkler, Carsten, 2013. "Bootstrap Co-integration Rank Testing: The Effect of Bias-Correcting Parameter Estimates," Working Papers 32993, University of Mannheim, Department of Economics.
  3. Christian Kascha & Carsten Trenkler, 2009. "Bootstrapping the likelihood ratio cointegration test in error correction models with unknown lag order," Working Paper 2009/12, Norges Bank.

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