Markov chain Monte Carlo methods for stochastic volatility models

Abstract

This paper is concerned with simulation-based inference in generalized models of stochastic volatility defined by heavy-tailed Student-t distributions (with unknown degrees of freedom) and exogenous variables in the observation and volatility equations and a jump component in the observation equation. By building on the work of Kim, Shephard and Chib (Rev. Econom. Stud. 65 (1998) 361), we develop efficient Markov chain Monte Carlo algorithms for estimating these models. The paper also discusses how the likelihood function of these models can be computed by appropriate particle filter methods. Computation of the marginal likelihood by the method of Chib (J. Amer. Statist. Assoc. 90 (1995) 131..