An effcient exact Bayesian method For state space models with stochastic volatility

Abstract

Abstract This paper introduces a Bayesian MCMC method, referred to as a marginalized mixture sampler, for state space models whose disturbances follow stochastic volatility processes. The marginalized mixture sampler is based on a mixture-normal approximation of the log-χ 2 distribution, but it is implemented without the need to simulate the mixture indicator variable. The key innovation is to use the filter ing scheme developed by Kim (Kim C.-J. 1994. “Dynamic Linear Models with Markov-Switching.” Journal of Econometrics 60: 1–22.) and the forward-filtering backward-sampling algorithm to generate a proposal series of the latent stochastic volatility process. The proposal series is then accepted according to the Metropolis-Hastings acceptance probability. The new sampler is examined within an unobserved component model and a time-varying parameter vector autoregressive model, and it reduces substantially the correlations between MCMC draws.