Efficient importance variational approximations for state space models

Variational methods are a potentially scalable estimation approach for state space models. However, existing methods are inaccurate or computationally infeasible for many state space models. This article 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. Our approach constructs a variational approximation to the states that is close to the exact conditional posterior distribution of the states using insights from the efficient importance sampling literature. 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.