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Bayesian semiparametric multivariate GARCH modeling

  • Mark J. Jensen
  • John M. Maheu

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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File URL: http://www.frbatlanta.org/documents/pubs/wp/wp1209.pdf
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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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  14. Mark J. Jensen & John M. Maheu, 2008. "Bayesian semiparametric stochastic volatility modeling," Working Paper 2008-15, Federal Reserve Bank of Atlanta.
  15. Silvennoinen, Annastiina & Teräsvirta, Timo, 2007. "Multivariate GARCH models," SSE/EFI Working Paper Series in Economics and Finance 669, Stockholm School of Economics, revised 18 Jan 2008.
  16. 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.
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  19. K. Diamantopoulos & I. Vrontos, 2010. "A Student-t Full Factor Multivariate GARCH Model," Computational Economics, Society for Computational Economics, vol. 35(1), pages 63-83, January.
  20. 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.
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