  An MCMC simulation method based on a two stage delayed rejection
Metropolis-Hastings algorithm is proposed to estimate a factor multivariate
stochastic volatility model. The first stage uses kstep iteration towards the
mode, with k small, and the second stage uses an adaptive random walk proposal
density. The marginal likelihood approach of Chib (1995) is used to choose the
number of factors, with the posterior density ordinates approximated by
Gaussian copula. Simulation and real data applications suggest that the
proposed simulation method is computationally much more efficient than the
approach of Chib. Nardari and Shephard (2006}. This increase in computational
efficiency is particularly important in calculating marginal likelihoods
because it is necessary to carry out the simulation a number of times to
estimate the posterior ordinates for a given marginal likelihood. In addition
to the MCMC method, the paper also proposes a fast approximate EM method to
estimate the factor multivariate stochastic volatility model. The estimates
from the approximate EM method are of interest in their own right, but are
especially useful as initial inputs to MCMC methods, making them more efficient
computationally. The methodology is illustrated using simulated and real
examples.
