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Bayesian clustering of many GARCH models

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  • BAUWENS, Luc
  • ROMBOUTS, Jeroen

Abstract

We consider the estimation of a large number of GARCH models, of the order of several hundreds. To achieve parsimony, we classify the series in a small number of groups. Within a cluster, the series share the same model and the same parameters. Each cluster contains therefore similar series. We do not know a priori which series belongs to which cluster. The model is a finite mixture of distributions, where the component weights are unknown parameters and each component distribution has its own conditional mean and variance. Inference is done by the Bayesian approach, using data augmentation techniques. Illustrations are provided.

Suggested Citation

  • BAUWENS, Luc & ROMBOUTS, Jeroen, 2003. "Bayesian clustering of many GARCH models," LIDAM Discussion Papers CORE 2003087, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2003087
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    References listed on IDEAS

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    1. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    2. Robert, Christian P. & Mengersen, Kerrie L., 1999. "Reparameterisation Issues in Mixture Modelling and their bearing on MCMC algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 29(3), pages 325-343, January.
    3. Bauwens, Luc & Lubrano, Michel & Richard, Jean-Francois, 2000. "Bayesian Inference in Dynamic Econometric Models," OUP Catalogue, Oxford University Press, number 9780198773139.
    4. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    5. Chib, Siddhartha & Hamilton, Barton H., 2000. "Bayesian analysis of cross-section and clustered data treatment models," Journal of Econometrics, Elsevier, vol. 97(1), pages 25-50, July.
    6. Kearney, Colm & Patton, Andrew J, 2000. "Multivariate GARCH Modeling of Exchange Rate Volatility Transmission in the European Monetary System," The Financial Review, Eastern Finance Association, vol. 35(1), pages 29-48, February.
    7. Tse, Y K & Tsui, Albert K C, 2002. "A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model with Time-Varying Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 351-362, July.
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    Citations

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    Cited by:

    1. Christian Francq & Lajos Horváth, 2011. "Merits and Drawbacks of Variance Targeting in GARCH Models," Journal of Financial Econometrics, Oxford University Press, vol. 9(4), pages 619-656.
    2. Cavit Pakel & Neil Shephard & Kevin Sheppard, 2009. "Nuisance parameters, composite likelihoods and a panel of GARCH models," OFRC Working Papers Series 2009fe03, Oxford Financial Research Centre.
    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. Barigozzi, Matteo & Brownlees, Christian & Gallo, Giampiero M. & Veredas, David, 2014. "Disentangling systematic and idiosyncratic dynamics in panels of volatility measures," Journal of Econometrics, Elsevier, vol. 182(2), pages 364-384.
    5. Robert Darkins & Emma J Cooke & Zoubin Ghahramani & Paul D W Kirk & David L Wild & Richard S Savage, 2013. "Accelerating Bayesian Hierarchical Clustering of Time Series Data with a Randomised Algorithm," PLOS ONE, Public Library of Science, vol. 8(4), pages 1-9, April.
    6. Juarez, Miguel A. & Steel, Mark F. J., 2006. "Model-based Clustering of non-Gaussian Panel Data," MPRA Paper 880, University Library of Munich, Germany.
    7. Bonato, Matteo & Caporin, Massimiliano & Ranaldo, Angelo, 2013. "Risk spillovers in international equity portfolios," Journal of Empirical Finance, Elsevier, vol. 24(C), pages 121-137.
    8. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    9. Sylvia Frühwirth-Schnatter, 2011. "Panel data analysis: a survey on model-based clustering of time series," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 5(4), pages 251-280, December.
    10. Christian T. Brownlees & Fabrizio Cipollini & Giampiero M. Gallo, 2011. "Multiplicative Error Models," Econometrics Working Papers Archive 2011_03, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti", revised Apr 2011.
    11. Baltodano López, Ovielt & Billio, Monica & Casarin, Roberto & Costola, Michele, 2025. "Compounding geopolitical and energy risks: A clustered stochastic multi-COVOL model," Energy Economics, Elsevier, vol. 149(C).
    12. Brownlees, Christian T., 2019. "Hierarchical GARCH," Journal of Empirical Finance, Elsevier, vol. 51(C), pages 17-27.
    13. Rombouts, Jeroen V.K. & Stentoft, Lars, 2015. "Option pricing with asymmetric heteroskedastic normal mixture models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 635-650.
    14. Aielli, Gian Piero & Caporin, Massimiliano, 2014. "Variance clustering improved dynamic conditional correlation MGARCH estimators," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 556-576.
    15. Pietro Coretto & Michele La Rocca & Giuseppe Storti, 2020. "Improving Many Volatility Forecasts Using Cross-Sectional Volatility Clusters," JRFM, MDPI, vol. 13(4), pages 1-23, March.
    16. Jane L. Harvill & Priya Kohli & Nalini Ravishanker, 2017. "Clustering Nonlinear, Nonstationary Time Series Using BSLEX," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 935-955, September.
    17. Rombouts Jeroen V. K. & Bouaddi Mohammed, 2009. "Mixed Exponential Power Asymmetric Conditional Heteroskedasticity," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(3), pages 1-32, May.

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    Keywords

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    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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