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Bayesian Estimation of Generalized Hyperbolic Skewed Student GARCH Models

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Abstract

Efficient posterior simulators for two GARCH models with generalized hyperbolic disturbances are presented. The first model, GHt-GARCH, is a threshold GARCH with a skewed and heavy-tailed error distribution; in this model, the latent variables that account for skewness and heavy tails are identically and independently distributed. The second model, ODLV-GARCH, is formulated in terms of observation-driven latent variables; it automatically incorporates a risk premium effect. Both models nest the ordinary threshold t-GARCH as a limiting case. The GHt-GARCH and ODLV-GARCH models are compared with each other and with the threshold t-GARCH using five publicly available asset return data sets, by means of Bayes factors, information criteria, and classical forecast evaluation tools. The GHt-GARCH and ODLV-GARCH models both strongly dominate the threshold t-GARCH, and the Bayes factors generally favor GHt-GARCH over ODLV-GARCH. A Markov switching extension of GHt-GARCH is also presented. This extension is found to be an empirical improvement over the single-regime model for one of the five data sets.

Suggested Citation

  • Deschamps, Philippe J., 2011. "Bayesian Estimation of Generalized Hyperbolic Skewed Student GARCH Models," DQE Working Papers 16, Department of Quantitative Economics, University of Freiburg/Fribourg Switzerland, revised 09 Jun 2012.
  • Handle: RePEc:fri:dqewps:wp0016
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    Cited by:

    1. Deniz Erdemlioglu & Sébastien Laurent & Christopher J. Neely, 2013. "Econometric modeling of exchange rate volatility and jumps," Chapters,in: Handbook of Research Methods and Applications in Empirical Finance, chapter 16, pages 373-427 Edward Elgar Publishing.
    2. Deschamps, P., 2015. "Alternative Formulation of the Leverage Effect in a Stochastic Volatility Model with Asymmetric Heavy-Tailed Errors," CORE Discussion Papers 2015020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Patricia Lengua & Cristian Bayes & Gabriel Rodríguez, 2015. " A Stochastic Volatility Model with GH Skew Student’s t-Distribution: Application to Latin-American Stock Returns," Documentos de Trabajo / Working Papers 2015-405, Departamento de Economía - Pontificia Universidad Católica del Perú.

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    Keywords

    Autoregressive conditional heteroskedasticity; Markov chain Monte Carlo; bridge sampling; heavy-tailed skewed distributions; generalized hyperbolic distribution; generalized inverse Gaussian distribution;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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