Sequential Bayesian Inference for Static Parameters in Dynamic State Space Models

A method for sequential Bayesian inference of the static parameters of a dynamic state space model is proposed. The method is able to use any valid approximation to the filtering and prediction densities of the state process. It computes the posterior distribution of the static parameters on a discrete grid that tracks the support dynamically. For inference of the state process, the Kalman filter and its extensions as well as cubature filtering have been used. It is illustrated with several examples including the stochastic volatility model and the challenging Kitagawa model and is compared to both online and offline methods. It is shown to provide a good trade off between speed and performance.