Decomposition of time series models in state-space form

This paper gives a methodology for decompositions of a very wide class of time series, including normal and non-normal time series, which are represented in state-space form. In particular the linked signals generated from dynamic generalized linear models are decomposed into a suitable sum of noise-free dynamic linear models. A number of relevant general results are given and two important cases, consisting of normally distributed data and binomially distributed data, are examined in detail. The methods are illustrated by considering examples involving both linear trend and seasonal component time series. Some keywords: Decompositions of time series, dynamic models, generalized linear models, Bayesian forecasting, state space models, Kalman filtering.