Identifiability Conditions for Spatio-Temporal Bayesian Dynamic Linear Models

In this paper a class of models for Gaussian space-time processes is considered in a state--space setup. The observed process is assumed to be the sum of unobservable components, such as a trend, a periodic component, a stationary autoregressive component and a measurement error. Although only the space--time structure of the stationary component is treated explicitly, it can be shown that it is possible to deal with spatial interaction among nonstationary components too. The inclusion of explanatory variables is considered, which can be suitable for both control policies and spatial prediction. Since in real applications such models can be considerably complex, our attention focuses on identifiability conditions.