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Bayesian semiparametric multivariate GARCH modeling

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  • Mark J. Jensen
  • John M. Maheu

Abstract

This paper proposes a Bayesian nonparametric modeling approach for the return distribution in multivariate GARCH models. In contrast to the parametric literature, the return distribution can display general forms of asymmetry and thick tails. An infinite mixture of multivariate normals is given a flexible Dirichlet process prior. The GARCH functional form enters into each of the components of this mixture. We discuss conjugate methods that allow for scale mixtures and nonconjugate methods, which provide mixing over both the location and scale of the normal components. MCMC methods are introduced for posterior simulation and computation of the predictive density. Bayes factors and density forecasts with comparisons to GARCH models with Student-t innovations demonstrate the gains from our flexible modeling approach.

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Bibliographic Info

Paper provided by Federal Reserve Bank of Atlanta in its series Working Paper with number 2012-09.

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Date of creation: 2012
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Handle: RePEc:fip:fedawp:2012-09

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  1. Galeano, Pedro & Ausín, M. Concepción, 2010. "The Gaussian Mixture Dynamic Conditional Correlation Model: Parameter Estimation, Value at Risk Calculation, and Portfolio Selection," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 559-571.
  2. Concepción Ausín & Pedro Galeano & Pulak Ghosh, 2010. "A semiparametric Bayesian approach to the analysis of financial time series with applications to value at risk estimation," Statistics and Econometrics Working Papers ws103822, Universidad Carlos III, Departamento de Estadística y Econometría.
  3. I. D. Vrontos & P. Dellaportas & D. N. Politis, 2003. "A full-factor multivariate GARCH model," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 312-334, December.
  4. Silvennoinen, Annastiina & Teräsvirta, Timo, 2007. "Multivariate GARCH models," Working Paper Series in Economics and Finance 669, Stockholm School of Economics, revised 18 Jan 2008.
  5. Hafner, Christian M. & Rombouts, Jeroen V.K., 2007. "Semiparametric Multivariate Volatility Models," Econometric Theory, Cambridge University Press, vol. 23(02), pages 251-280, April.
  6. Harvey, A. C. & Ruiz, Esther & Sentana, E., 1992. "Unobserved Component Time Series Models with ARCH Disturbances," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4702, Universidad Carlos III de Madrid.
  7. Mark J. Jensen & John M. Maheu, 2009. "Bayesian Semiparametric Stochastic Volatility Modeling," Working Paper Series 23_09, The Rimini Centre for Economic Analysis, revised Jan 2009.
  8. Osiewalski, Jacek & Pipien, Mateusz, 2004. "Bayesian comparison of bivariate ARCH-type models for the main exchange rates in Poland," Journal of Econometrics, Elsevier, vol. 123(2), pages 371-391, December.
  9. Andrea Buraschi & Paolo Porchia & Fabio Trojani, 2010. "Correlation Risk and Optimal Portfolio Choice," Journal of Finance, American Finance Association, vol. 65(1), pages 393-420, 02.
  10. P. Dellaportas & I. D. Vrontos, 2007. "Modelling volatility asymmetries: a Bayesian analysis of a class of tree structured multivariate GARCH models," Econometrics Journal, Royal Economic Society, vol. 10(3), pages 503-520, November.
  11. Diks, Cees & Panchenko, Valentyn & van Dijk, Dick, 2011. "Likelihood-based scoring rules for comparing density forecasts in tails," Journal of Econometrics, Elsevier, vol. 163(2), pages 215-230, August.
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Cited by:
  1. Xibin Zhang & Maxwell L. King, 2011. "Bayesian semiparametric GARCH models," Monash Econometrics and Business Statistics Working Papers 24/11, Monash University, Department of Econometrics and Business Statistics.
  2. Audrone Virbickaite & M. Concepci\'on Aus\'in & Pedro Galeano, 2013. "Bayesian Non-Parametric Portfolio Decisions with Financial Time Series," Papers 1301.5129, arXiv.org.

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