Bayesian Inference for Mixtures of Stable Distributions

Cahier du CEREMADE No. 0428

50 Pages Posted: 9 Mar 2006

See all articles by Roberto Casarin

Roberto Casarin

University Ca' Foscari of Venice - Department of Economics

Date Written: 2004

Abstract

In many different fields such as hydrology, telecommunications, physics of condensed matter and finance, the gaussian model results unsatisfactory and reveals difficulties in fitting data with skewness, heavy tails and multimodality. The use of stable distributions allows for modelling skewness and heavy tails but gives rise to inferential problems related to the estimation of the stable distributions' parameters. Some recent works have proposed characteristic function based estimation method and MCMC simulation based estimation techniques like the MCMC-EM method and the Gibbs sampling method in a full Bayesian approach. The aim of this work is to generalise the stable distribution framework by introducing a model that accounts also for multimodality. In particular we introduce a stable mixture model and a suitable reparametrisation of the mixture, which allow us to make inference on the mixture parameters. We use a full Bayesian approach and MCMC simulation techniques for the estimation of the posterior distribution. Finally we propose some applications of stable mixtures to financial data.

Keywords: Mixture model, Stable distributions, Bayesian inference, Gibbs sampling

JEL Classification: C11, C12, C13, C63

Suggested Citation

Casarin, Roberto, Bayesian Inference for Mixtures of Stable Distributions (2004). Cahier du CEREMADE No. 0428, Available at SSRN: https://ssrn.com/abstract=739791 or http://dx.doi.org/10.2139/ssrn.739791

Roberto Casarin (Contact Author)

University Ca' Foscari of Venice - Department of Economics ( email )

San Giobbe 873/b
Venice, 30121
Italy
+39 030.298.91.49 (Phone)
+39 030.298.88.37 (Fax)

HOME PAGE: http://sites.google.com/view/robertocasarin

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
144
Abstract Views
905
rank
247,244
PlumX Metrics