Spatio-temporal change-point modeling

There is by now a substantial literature on spatio-temporal modeling. However, to date, there exists essentially no literature which addresses the issue of process change from a certain time. In fact, if we look at change points for purely time series data, the customary form is to propose a model involving a mean or level shift. We see little attempting to capture a change in association structure. Part of the concern is how to specify flexible ways to bridge the association across the time point and still ensure that a proper joint distribution has been defined for all of the data. Introducing a spatial component evidently adds further complication. We want to allow for a change-point reflecting change in both temporal and spatial association. In this paper we propose a constructive, flexible model formulation through additive specifications. We also demonstrate how computational concerns benefit from the availability of temporal order. Finally, we illustrate with several simulated datasets to examine the capability of the model to detect different types of structural changes.