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

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Date of creation: 2012
Date of revision:
Handle: RePEc:fip:fedawp:2012-09
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  1. Bauwens, L. & Hafner, C.M. & Rombouts, J.V.K., 2007. "Multivariate mixed normal conditional heteroskedasticity," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3551-3566, April.
  2. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
  3. Ledoit, Olivier & Santa-Clara, Pedro & Wolf, Michael, 1999. "Flexible Multivariate GARCH Modeling With an Application to International Stock Markets," University of California at Los Angeles, Anderson Graduate School of Management qt93s6p8gb, Anderson Graduate School of Management, UCLA.
  4. 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.
  5. Mark J. Jensen & John M. Maheu, 2012. "Estimating a semiparametric asymmetric stochastic volatility model with a Dirichlet process mixture," FRB Atlanta Working Paper 2012-06, Federal Reserve Bank of Atlanta.
  6. Fiorentini, Gabriele & Sentana, Enrique & Calzolari, Giorgio, 2003. "Maximum Likelihood Estimation and Inference in Multivariate Conditionally Heteroscedastic Dynamic Regression Models with Student t Innovations," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 532-46, October.
  7. Rombouts, Jeroen V. K. & Hafner, Christian M., 2004. "Semiparametric multivariate volatility models," Papers 2004,14, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE).
  8. Bauwens, Luc & Laurent, Sebastien, 2005. "A New Class of Multivariate Skew Densities, With Application to Generalized Autoregressive Conditional Heteroscedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 346-354, July.
  9. Long, Xiangdong & Su, Liangjun & Ullah, Aman, 2011. "Estimation and Forecasting of Dynamic Conditional Covariance: A Semiparametric Multivariate Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 109-125.
  10. 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.
  11. 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.
  12. Mark J. Jensen & John M. Maheu, 2008. "Bayesian semiparametric stochastic volatility modeling," FRB Atlanta Working Paper 2008-15, Federal Reserve Bank of Atlanta.
  13. 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.
  14. Koop, Gary & Korobilis, Dimitris, 2009. "Bayesian Multivariate Time Series Methods for Empirical Macroeconomics," MPRA Paper 20125, University Library of Munich, Germany.
  15. Harvey, Andrew & Ruiz, Esther & Sentana, Enrique, 1992. "Unobserved component time series models with Arch disturbances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 129-157.
  16. 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.
  17. Brent Hudson & Richard Gerlach, 2008. "A Bayesian approach to relaxing parameter restrictions in multivariate GARCH models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 17(3), pages 606-627, November.
  18. 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.
  19. Richardson, Matthew & Smith, Tom, 1993. "A Test for Multivariate Normality in Stock Returns," The Journal of Business, University of Chicago Press, vol. 66(2), pages 295-321, April.
  20. 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 116-31, February.
  21. 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.
  22. 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.
  23. Cees Diks & Valentyn Panchenko & Dick van Dijk, 2011. "Likelihood-based scoring rules for comparing density forecasts in tails," Post-Print peer-00834423, HAL.
  24. 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.
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