Efficient variational approximations for state space models

Abstract

Variational Bayes methods are a potential scalable estimation approach for state space models. However, existing methods are inaccurate or computationally infeasible for many state space models. This paper proposes a variational approximation that is accurate and fast for any model with a closed-form measurement density function and a state transition distribution within the exponential family of distributions. We show that our method can accurately and quickly estimate a multivariate Skellam stochastic volatility model with high-frequency tick-by-tick discrete price changes of four stocks, and a time-varying parameter vector autoregression with a stochastic volatility model using eight macroeconomic variables.