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Bayesian inference of multivariate-GARCH-BEKK models

Author

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  • G. C. Livingston

    (School of Information and Physical Sciences, The University of Newcastle, University Drive)

  • Darfiana Nur

    (Curtin University)

Abstract

The main aim of this paper is to present a Bayesian analysis of Multivariate GARCH(l, m) (M-GARCH) models including estimation of the coefficient parameters as well as the model order, by combining a set of existing MCMC algorithms in the literature. The proposed algorithm focuses on the BEKK formulation of the multivariate GARCH model. The estimation procedure will be designed as a custom MCMC with embedded Reversible Jump MCMC (RJMCMC) and Delayed Rejection Metropolis-Hastings (DRMH) steps implemented using the statistical software R. The RJMCMC steps allow three variants of BEKK models (constant, diagonal and full) to be indexed and this index included as a parameter to be estimated. The proposed MCMC algorithms are validated using extensive simulation experiments followed by a case study using bivariate data derived from the daily share prices for BHP Group Limited, Rio Tinto Group, and Fortescue Metals Group Limited on the ASX over from September 2013 to December 2021.

Suggested Citation

  • G. C. Livingston & Darfiana Nur, 2023. "Bayesian inference of multivariate-GARCH-BEKK models," Statistical Papers, Springer, vol. 64(5), pages 1749-1774, October.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:5:d:10.1007_s00362-022-01360-6
    DOI: 10.1007/s00362-022-01360-6
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    References listed on IDEAS

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    1. Sébastien Laurent & Jeroen V. K. Rombouts & Francesco Violante, 2012. "On the forecasting accuracy of multivariate GARCH models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 934-955, September.
    2. Jensen, Mark J. & Maheu, John M., 2013. "Bayesian semiparametric multivariate GARCH modeling," Journal of Econometrics, Elsevier, vol. 176(1), pages 3-17.
    3. Peter R. Hansen & Asger Lunde & James M. Nason, 2011. "The Model Confidence Set," Econometrica, Econometric Society, vol. 79(2), pages 453-497, March.
    4. Vrontos, I D & Dellaportas, P & Politis, D N, 2000. "Full Bayesian Inference for GARCH and EGARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 187-198, April.
    5. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    7. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-131, February.
    8. Peter Reinhard Hansen & Asger Lunde & James M. Nason, 2003. "Choosing the Best Volatility Models: The Model Confidence Set Approach," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(s1), pages 839-861, December.
    9. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    10. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    11. Hong Li, 2007. "International linkages of the Chinese stock exchanges: a multivariate GARCH analysis," Applied Financial Economics, Taylor & Francis Journals, vol. 17(4), pages 285-297.
    12. Kearney, Colm & Patton, Andrew J, 2000. "Multivariate GARCH Modeling of Exchange Rate Volatility Transmission in the European Monetary System," The Financial Review, Eastern Finance Association, vol. 35(1), pages 29-48, February.
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    Cited by:

    1. Qingrui Wang & Zhao Yao, 2025. "Bayesian influence diagnostics for a multivariate GARCH model," Statistical Papers, Springer, vol. 66(2), pages 1-27, February.

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