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Bayesian estimation of the gaussian mixture garch model

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  • Ausín Olivera, María Concepción
  • Galeano, Pedro

Abstract

In this paper, we perform Bayesian inference and prediction for a GARCH model where the innovations are assumed to follow a mixture of two Gaussian distributions. This GARCH model can capture the patterns usually exhibited by many financial time series such as volatility clustering, large kurtosis and extreme observations. A Griddy-Gibbs sampler implementation is proposed for parameter estimation and volatility prediction. The method is illustrated using the Swiss Market Index.

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  • Ausín Olivera, María Concepción & Galeano, Pedro, 2005. "Bayesian estimation of the gaussian mixture garch model," DES - Working Papers. Statistics and Econometrics. WS ws053605, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws053605
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    Cited by:

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    2. Virbickaitė, Audronė & Ausín, M. Concepción & Galeano, Pedro, 2016. "A Bayesian non-parametric approach to asymmetric dynamic conditional correlation model with application to portfolio selection," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 814-829.
    3. Rombouts, Jeroen V.K. & Stentoft, Lars, 2014. "Bayesian option pricing using mixed normal heteroskedasticity models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 588-605.
    4. Xi, Yanhui & Peng, Hui & Qin, Yemei & Xie, Wenbiao & Chen, Xiaohong, 2015. "Bayesian analysis of heavy-tailed market microstructure model and its application in stock markets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 117(C), pages 141-153.
    5. Ardia, David & Hoogerheide, Lennart F., 2010. "Efficient Bayesian estimation and combination of GARCH-type models," MPRA Paper 22919, University Library of Munich, Germany.
    6. Ausín, M. Concepción & Galeano, Pedro & Ghosh, Pulak, 2014. "A semiparametric Bayesian approach to the analysis of financial time series with applications to value at risk estimation," European Journal of Operational Research, Elsevier, vol. 232(2), pages 350-358.
    7. Broda, Simon A. & Haas, Markus & Krause, Jochen & Paolella, Marc S. & Steude, Sven C., 2013. "Stable mixture GARCH models," Journal of Econometrics, Elsevier, vol. 172(2), pages 292-306.
    8. García de la Fuente, Cristina & Galeano San Miguel, Pedro & Wiper, Michael Peter, 2014. "Bayesian estimation of a dynamic conditional correlation model with multivariate Skew-Slash innovations," DES - Working Papers. Statistics and Econometrics. WS ws141711, Universidad Carlos III de Madrid. Departamento de Estadística.
    9. Borowska, Agnieszka & Hoogerheide, Lennart & Koopman, Siem Jan & van Dijk, Herman K., 2020. "Partially censored posterior for robust and efficient risk evaluation," Journal of Econometrics, Elsevier, vol. 217(2), pages 335-355.
    10. Dinghai Xu, 2009. "The Applications of Mixtures of Normal Distributions in Empirical Finance: A Selected Survey," Working Papers 0904, University of Waterloo, Department of Economics, revised Sep 2009.
    11. Baştürk, Nalan & Grassi, Stefano & Hoogerheide, Lennart & Opschoor, Anne & van Dijk, Herman K., 2017. "The R Package MitISEM: Efficient and Robust Simulation Procedures for Bayesian Inference," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 79(i01).
    12. Ha, Jeongcheol & Lee, Taewook, 2011. "NM-QELE for ARMA-GARCH models with non-Gaussian innovations," Statistics & Probability Letters, Elsevier, vol. 81(6), pages 694-703, June.
    13. Qiang Xia & Heung Wong & Jinshan Liu & Rubing Liang, 2017. "Bayesian Analysis of Power-Transformed and Threshold GARCH Models: A Griddy-Gibbs Sampler Approach," Computational Economics, Springer;Society for Computational Economics, vol. 50(3), pages 353-372, October.
    14. Massimiliano Caporin & Eduardo Rossi & Paolo Santucci De Magistris, 2014. "Chasing Volatility. A Persistent Multiplicative Error Model With Jumps," "Marco Fanno" Working Papers 0186, Dipartimento di Scienze Economiche "Marco Fanno".
    15. Yuzhi Cai, 2021. "Estimating expected shortfall using a quantile function model," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(3), pages 4332-4360, July.
    16. Haas, Markus & Mittnik, Stefan & Paolella, Marc S., 2009. "Asymmetric multivariate normal mixture GARCH," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2129-2154, April.
    17. Ardia, David & Baştürk, Nalan & Hoogerheide, Lennart & van Dijk, Herman K., 2012. "A comparative study of Monte Carlo methods for efficient evaluation of marginal likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3398-3414.
    18. Vica Tendenan & Richard Gerlach & Chao Wang, 2020. "Tail risk forecasting using Bayesian realized EGARCH models," Papers 2008.05147, arXiv.org, revised Aug 2020.
    19. Bentarzi, M. & Hamdi, F., 2008. "Mixture periodic autoregressive conditional heteroskedastic models," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 1-16, September.
    20. Dellaportas, Petros & Tsionas, Mike G., 2019. "Importance sampling from posterior distributions using copula-like approximations," Journal of Econometrics, Elsevier, vol. 210(1), pages 45-57.
    21. Abdullah Alqahtani & Julien Chevallier, 2020. "Dynamic Spillovers between Gulf Cooperation Council’s Stocks, VIX, Oil and Gold Volatility Indices," JRFM, MDPI, vol. 13(4), pages 1-17, April.
    22. Chen, Yan & Yu, Wenqiang, 2020. "Setting the margins of Hang Seng Index Futures on different positions using an APARCH-GPD Model based on extreme value theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    23. Giannikis, D. & Vrontos, I.D. & Dellaportas, P., 2008. "Modelling nonlinearities and heavy tails via threshold normal mixture GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1549-1571, January.
    24. Ausin, M. Concepcion & Lopes, Hedibert F., 2010. "Time-varying joint distribution through copulas," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2383-2399, November.

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