Variational Approximation of Factor Stochastic Volatility Models

Estimation and prediction in high dimensional multivariate factor stochastic volatility models is an important and active research area because they allow a parsimonious representation of multivariate stochastic volatility. Such factor models are usually estimated by Markov chain Monte Carlo or particle methods, which are usually slow for high dimensional or long time series because of the large number of parameters and latent states involved. Our article proposes fast batch and sequential variational methods to approximate the posterior distribution of the states and parameters in a factor stochastic volatility model. It also obtains one-step and multi-step ahead variational forecast distributions. The method is 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 is much faster.