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Bootstrap determination of the co-integration rank in VAR models

Author

Listed:
  • Giuseppe Cavaliere

    (Università di Bologna)

  • Anders Rahbek
  • Taylor A.M.Robert

Abstract

This paper discusses a consistent bootstrap implementation of the likelihood ratio [LR] co-integration rank test and associated sequential rank determination procedure of Johansen (1996). The bootstrap samples are constructed using the restricted parameter estimates of the underlying VAR model which obtain under the reduced rank null hypothesis. A full asymptotic theory is provided which shows that, unlike the bootstrap procedure in Swensen (2006) where a combination of unrestricted and restricted estimates from the VAR model is used, the resulting bootstrap data are I(1) and satisfy the null co-integration rank, regardless of the true rank. This ensures that the bootstrap LR test is asymptotically correctly sized and that the probability that the bootstrap sequential procedure selects a rank smaller than the true rank converges to zero. Monte Carlo evidence suggests that our bootstrap procedures work very well in practice.

Suggested Citation

  • Giuseppe Cavaliere & Anders Rahbek & Taylor A.M.Robert, 2011. "Bootstrap determination of the co-integration rank in VAR models," Quaderni di Dipartimento 9, Department of Statistics, University of Bologna.
    • Handle: RePEc:bot:quadip:wpaper:113
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    Citations

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    Cited by:

    1. Søren Johansen, 2014. "Times Series: Cointegration," CREATES Research Papers 2014-38, Department of Economics and Business Economics, Aarhus University.
    2. 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.
    3. Johansen, Søren & Nielsen, Morten Ørregaard, 2018. "The cointegrated vector autoregressive model with general deterministic terms," Journal of Econometrics, Elsevier, vol. 202(2), pages 214-229.
    4. Schreiber, Sven, 2018. "Are bootstrapped cointegration test findings unreliable?," Discussion Papers 2018/8, Free University Berlin, School of Business & Economics.
    5. Nielsen, Heino Bohn & Rahbek, Anders, 2014. "Unit root vector autoregression with volatility induced stationarity," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 144-167.

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