ABSTRACT
This chapter extends the state-space model to cases where the system noise and/or the observation noise are non-Gaussian. This non-Gaussian model is applicable when there are sudden changes in the parameters caused by structural changes of the system or by outliers in the time series. For the general non-Gaussian models considers, the Kalman filtering and the smoothing algorithms sometimes cannot yield good estimates of the state. The state-space model is a very useful tool for time series modeling, since it is a natural representation of a time series model and provides us with very efficient computational methods such as Kalman filtering and smoothing algorithms. While a linear-Gaussian state-space model can reasonably express gradual structural changes of nonstationary time series, it is necessary to build a complex model to properly address abrupt changes.
