  Estimation and prediction in high dimensional multivariate factor stochastic
volatility models is an important and active research area because such models
allow a parsimonious representation of multivariate stochastic volatility.
Bayesian inference for factor stochastic volatility models is usually done by
Markov chain Monte Carlo methods, often by particle Markov chain Monte Carlo,
which are usually slow for high dimensional or long time series because of the
large number of parameters and latent states involved. Our article makes two
contributions. The first is to propose fast and accurate variational Bayes
methods to approximate the posterior distribution of the states and parameters
in factor stochastic volatility models. The second contribution is to extend
this batch methodology to develop fast sequential variational updates for
prediction as new observations arrive. The methods are applied to simulated and
real datasets and shown to produce good approximate inference and prediction
compared to the latest particle Markov chain Monte Carlo approaches, but are
much faster.
