  In this paper we develop a Bayesian procedure for estimating multivariate
stochastic volatility (MSV) using state space models. A multiplicative model
based on inverted Wishart and multivariate singular beta distributions is
proposed for the evolution of the volatility, and a flexible sequential
volatility updating is employed. Being computationally fast, the resulting
estimation procedure is particularly suitable for on-line forecasting. Three
performance measures are discussed in the context of model selection: the
log-likelihood criterion, the mean of standardized one-step forecast errors,
and sequential Bayes factors. Finally, the proposed methods are applied to a
data set comprising eight exchange rates vis-a-vis the US dollar.
