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Bayesian inference on GARCH models using the Gibbs sampler

Author

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  • LUC BAUWENS
  • MICHEL LUBRANO

Abstract

This paper explains how the Gibbs sampler can be used to perform Bayesian inference on GARCH models. Although the Gibbs sampler is usually based on the analyti-cal knowledge of the full conditional posterior densities, such knowledge is not available in regression models with GARCH errors. We show that the Gibbs sampler can be combined with a unidimensional deterministic integration rule applied to each coordinate of the poste-rior density. The full conditional densities are evaluated and inverted numerically to obtain random draws of the joint posterior. The method is shown to be feasible and competitive compared with importance sampling and the Metropolis-Hastings algorithm. It is applied to estimate an asymmetric Student-GARCH model for the return on a stock exchange index, and to compute predictive option prices on the index. We prove, moreover, that a flat prior on the degrees of freedom parameter leads to an improper posterior density.

Suggested Citation

  • Luc Bauwens & Michel Lubrano, 1998. "Bayesian inference on GARCH models using the Gibbs sampler," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages 23-46.
  • Handle: RePEc:ect:emjrnl:v:1:y:1998:i:conferenceissue:p:c23-c46
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    More about this item

    Keywords

    Bayesian inference; GARCH; Gibbs sampler; Monte Carlo; Option pricing.;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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