Bayesian state space modeling for nonlinear nonstationary time series

Bayesian time series modeling can be achieved by general state space model. Recursive filtering and smoothing formula corresponding to the Kalman filter and smoother can be obtained for the general state space model, and can be realized by the implementations based on numerical integration or Monte Carlo approximation. Selection among the possible candidate models can be done by the information criterion AIC. When we need to use the Monte Carlo filter, we may have difficulty in parameter estimation, since the computed log-likelihood contains a sampling error. For such a situation, we also developed a self-adjusting state space model, with which the state and unknown parameters are simultaneously estimated. Numerical examples clearly shows the usefulness of the developed method.