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

Author

Listed:
  • 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.

Suggested Citation

  • Guiseppe Cavaliere & Anders Rahbek & A.M.Robert Taylor, 2010. "Bootstrap Sequential Determination of the Co-integration Rank in VAR Models," CREATES Research Papers 2010-07, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2010-07
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    References listed on IDEAS

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    1. 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.
    2. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    3. 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.
    4. 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, September.
    5. Goncalves, Silvia & Kilian, Lutz, 2004. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 123(1), pages 89-120, November.
    6. Cavaliere, Giuseppe & Rahbek, Anders & Taylor, A.M. Robert, 2010. "Testing for co-integration in vector autoregressions with non-stationary volatility," Journal of Econometrics, Elsevier, vol. 158(1), pages 7-24, September.
    7. 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.
    8. Cavaliere, Giuseppe & Rahbek, Anders & Taylor, A.M. Robert, 2010. "Cointegration Rank Testing Under Conditional Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 26(06), pages 1719-1760, December.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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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    Cited by:

    1. Kascha, Christian & Trenkler, Carsten, 2011. "Bootstrapping the likelihood ratio cointegration test in error correction models with unknown lag order," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1008-1017, February.
    2. Swensen, Anders Rygh, 2011. "A bootstrap algorithm for testing cointegration rank in VAR models in the presence of stationary variables," Journal of Econometrics, Elsevier, vol. 165(2), pages 152-162.
    3. 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).
    4. Giuseppe Cavaliere & A. M. Robert Taylor & Carsten Trenkler, 2015. "Bootstrap Co-integration Rank Testing: The Effect of Bias-Correcting Parameter Estimates," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(5), pages 740-759, October.

    More about this item

    Keywords

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

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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