Bayesian inference methods for univariate and multivariate GARCH Models: a Survey Articles uri icon

publication date

  • February 2015

start page

  • 76

end page

  • 96

issue

  • 1

volume

  • 29

international standard serial number (ISSN)

  • 0950-0804

electronic international standard serial number (EISSN)

  • 1467-6419

abstract

  • This survey reviews the existing literature on the most relevant Bayesian inference methods for univariate and multivariate GARCH models. The advantages and drawbacks of each procedure are outlined as well as the advantages of the Bayesian approach versus classical procedures. The paper makes emphasis on recent Bayesian non-parametric approaches for GARCH models that avoid imposing arbitrary parametric distributional assumptions. These novel approaches implicitly assume infinite mixture of Gaussian distributions on the standardized returns which have been shown to be more flexible and describe better the uncertainty about future volatilities. Finally, the survey presents an illustration using real data to show the flexibility and usefulness of the non-parametric approach.

keywords

  • autoregressive conditional heteroscedasticity; nonparametric problems; stochastic volatility; portfolio selection; generalized arch; exchange-rates; mixture; heteroskedasticity; covariances; returns