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Bootstrap Determination of the Co-integration Rank in Heteroskedastic 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 and Granger Centre for Time Series Econometrics, University of Nottingham)

Abstract

In a recent paper Cavaliere et al. (2012) develop bootstrap implementations of the (pseudo-) likelihood ratio [PLR] 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. They propose methods based on an i.i.d. bootstrap re-sampling scheme and establish the validity of their proposed bootstrap procedures in the context of a co-integrated VAR model with i.i.d. innovations. In this paper we investigate the properties of their bootstrap procedures, together with analogous procedures based on a wild bootstrap re-sampling scheme, when time-varying behaviour is present in either the conditional or unconditional variance of the innovations. We show that the bootstrap PLR tests are asymptotically correctly sized and, moreover, that the probability that the associated bootstrap sequential procedures select a rank smaller than the true rank converges to zero. This result is shown to hold for both the i.i.d. and wild bootstrap variants under conditional heteroskedasticity but only for the latter under unconditional heteroskedasticity. Monte Carlo evidence is reported which suggests that the bootstrap approach of Cavaliere et al. (2012) significantly improves upon the nite sample performance of corresponding procedures based on either the asymptotic PLR test or an alternative bootstrap method (where the short run dynamics in the VAR model are estimated unrestrictedly) for a variety of conditionally and unconditionally heteroskedastic innovation processes.

Suggested Citation

  • Giuseppe Cavaliere & Anders Rahbek & A.M.Robert Taylor, 2012. "Bootstrap Determination of the Co-integration Rank in Heteroskedastic VAR Models," Discussion Papers 12-11, University of Copenhagen. Department of Economics.
  • Handle: RePEc:kud:kuiedp:1211
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    1. repec:gam:jecnmx:v:5:y:2017:i:2:p:19-:d:98597 is not listed on IDEAS
    2. Boswijk, H. Peter & Cavaliere, Giuseppe & Rahbek, Anders & Taylor, A.M. Robert, 2016. "Inference on co-integration parameters in heteroskedastic vector autoregressions," Journal of Econometrics, Elsevier, vol. 192(1), pages 64-85.
    3. Cavaliere, Giuseppe & Nielsen, Morten Ørregaard & Taylor, A.M. Robert, 2015. "Bootstrap score tests for fractional integration in heteroskedastic ARFIMA models, with an application to price dynamics in commodity spot and futures markets," Journal of Econometrics, Elsevier, vol. 187(2), pages 557-579.
    4. Luca Benati & Robert Lucas, Jr. & Juan Nicolini & Warren Weber, 2016. "International Evidence on Long Run Money Demand," Working Papers id:11152, eSocialSciences.
    5. Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Carsten Jentsch & Dimitris N. Politis & Efstathios Paparoditis, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 416-441, May.
    6. Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Giuseppe Cavaliere & Anders Rahbek & A. M. Robert Taylor, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 272-289, May.
    7. 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.
    8. Phillips, Peter C.B. & Magdalinos, Tassos, 2013. "Inconsistent Var Regression With Common Explosive Roots," Econometric Theory, Cambridge University Press, vol. 29(04), pages 808-837, August.
    9. Michael T. Belongia & Peter N. Ireland, 2017. "The Demand for Divisia Money: Theory and Evidence," Boston College Working Papers in Economics 937, Boston College Department of Economics.
    10. repec:eee:econom:v:199:y:2017:i:1:p:49-62 is not listed on IDEAS
    11. Matei Demetrescu & Christoph Hanck & Adina I. Tarcolea, 2014. "Iv-Based Cointegration Testing In Dependent Panels With Time-Varying Variance," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(5), pages 393-406, August.
    12. 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.
    13. Benati, Luca, 2015. "The long-run Phillips curve: A structural VAR investigation," Journal of Monetary Economics, Elsevier, vol. 76(C), pages 15-28.
    14. repec:gam:jecnmx:v:5:y:2017:i:3:p:40-:d:110779 is not listed on IDEAS
    15. Luca Benati, 2017. "Cointegration Tests and the Classical Dichotomy," Diskussionsschriften dp1704, Universitaet Bern, Departement Volkswirtschaft.
    16. Jentsch, Carsten & Paparoditis, Efstathios & Politis, Dimitris N., 2014. "Block Bootstrap Theory for Multivariate Integrated and Cointegrated Processes," Working Papers 14-18, University of Mannheim, Department of Economics.
    17. Marcus J. Chambers, 2015. "A Jackknife Correction to a Test for Cointegration Rank," Econometrics, MDPI, Open Access Journal, vol. 3(2), pages 1-21, May.
    18. Ingrid Groessl & Artur Tarassow, 2015. "A Microfounded Model of Money Demand Under Uncertainty, and some Empirical Evidence," Macroeconomics and Finance Series 201504, University of Hamburg, Department of Socioeconomics, revised Jan 2018.
    19. Burak Eroglu, 2017. "Wavelet Variance Ratio Test And Wavestrapping For The Determination Of The Cointegration Rank," Working Papers 1706, The Center for Financial Studies (CEFIS), Istanbul Bilgi University.

    More about this item

    Keywords

    Bootstrap; Co-integration; Trace statistic; Rank determination; heteroskedasticity;

    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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