Non-Gaussian State-Space Model

In this chapter, we extend 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 pa-

rameters caused by structural changes of the system or by outliers in the

time series. For the general non-Gaussian models we consider here, it

may often be the case that we do not obtain good estimates of the state

by using Kalman filtering and the smoothing algorithms. Even in such

cases, however, we can derive a similar exact sequential formula to real-

ize filtering and smoothing algorithms using numerical integration.