Bayesian modelling volatility with mixture of α— stable distributions

摘要

In this paper we propose mixture models for dependent data in time series framework using a Bayesian approach. In particular we build a hidden Markov model with stationary distribution a finite mixtures of α-stable distributions to model time series volatility. Mixtures of α-stable distributions are a very general models that allow for skewness and heavy tails which have as special case the Normal mixtures models. The main problem related with α-stable distributions is the non existence of a close formula for the density function, in order to overcome these difficulies we adopt Markov chain Monte Carlo methods to generate sample for the posterior distribution of the parameters.