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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. Mark J. Jensen & John M. Maheu, 2008. "Bayesian semiparametric stochastic volatility modeling," Working Paper 2008-15, Federal Reserve Bank of Atlanta.
  2. 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.
  3. Jensen, Mark J. & Maheu, John M., 2014. "Estimating a semiparametric asymmetric stochastic volatility model with a Dirichlet process mixture," Journal of Econometrics, Elsevier, vol. 178(P3), pages 523-538.
  4. Hafner, C.M. & Rombouts, J.V.K., 2004. "Semiparametric multivariate volatility models," Econometric Institute Research Papers EI 2004-21, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  5. 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.
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  8. 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.
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  14. 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.
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  16. BAUWENS, Luc & LAURENT, Sébastien, . "A new class of multivariate skew densities, with application to generalized autoregressive conditional heteroscedasticity models," CORE Discussion Papers RP -1793, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  18. 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.
  19. 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.
  20. Gary Koop & Dimitris Korobilis, 2009. "Bayesian Multivariate Time Series Methods for Empirical Macroeconomics," Working Paper Series 47_09, The Rimini Centre for Economic Analysis, revised Jan 2009.
  21. 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.
  22. Annastiina Silvennoinen & Timo Teräsvirta, 2008. "Multivariate GARCH models," CREATES Research Papers 2008-06, School of Economics and Management, University of Aarhus.
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Citations

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Cited by:
  1. Jensen, Mark J & Maheu, John M, 2013. "Risk, Return and Volatility Feedback: A Bayesian Nonparametric Analysis," MPRA Paper 52132, University Library of Munich, Germany.
  2. 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.
  3. Audrone Virbickaite & M. Concepci\'on Aus\'in & Pedro Galeano, 2013. "A Bayesian Non-Parametric Approach to Asymmetric Dynamic Conditional Correlation Model With Application to Portfolio Selection," Papers 1301.5129, arXiv.org, revised Jan 2014.

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