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

Author

Listed:
  • Giuseppe Cavaliere

    (Department of Statistical Sciences, University of Bologna)

  • Anders Rahbek

    (Department of Economics, University of Copenhagen)

  • A. M. Robert Taylor

    (School of Economics, 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

  • Giuseppe Cavaliere & Anders Rahbek & A. M. Robert Taylor, 2010. "Bootstrap Sequential Determination of the Co-integration Rank in VAR Models," Discussion Papers 10-07, University of Copenhagen. Department of Economics.
    • Handle: RePEc:kud:kuiedp:1007
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Paolo Paruolo, 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.
    4. Bent Nielsen & Anders Rahbek, 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.
    5. Trenkler, Carsten, 2009. "Bootstrapping Systems Cointegration Tests With A Prior Adjustment For Deterministic Terms," Econometric Theory, Cambridge University Press, vol. 25(1), pages 243-269, February.
    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. 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.
    8. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2008. "Bootstrap Unit Root Tests For Time Series With Nonstationary Volatility," Econometric Theory, Cambridge University Press, vol. 24(1), pages 43-71, February.
    9. Cavaliere, Giuseppe & Rahbek, Anders & Taylor, A.M. Robert, 2010. "Cointegration Rank Testing Under Conditional Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 26(6), pages 1719-1760, December.
    10. 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.
    11. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    12. 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.
    13. 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.
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    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.
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    Cited by:

    1. Bicu, A.C. & Candelon, B., 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. 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.
    3. 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.
    4. 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.

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    More about this item

    Keywords

    co-integration; trace test; sequential rank determination; i.i.d. bootstrap; wild bootstrap;
    All these keywords.

    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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