Spatio-temporal analysis with short- and long-memory dependence: a state-space approach

Abstract

This paper deals with the estimation and prediction problems of spatio-temporal processes by using state-space methodology. The spatio-temporal process is represented through an infinite moving average decomposition. This expansion is well known in time series analysis and can be extended straightforwardly in space–time. Such an approach allows easy implementation of the Kalman filter procedure for estimation and prediction of linear time processes exhibiting both short- and long-range dependence and a spatial dependence structure given on the locations. Furthermore, we consider a truncated state-space equation, which allows to calculate an approximate likelihood for large data sets. The performance of the proposed Kalman filter approach is evaluated by means of several Monte Carlo experiments implemented under different scenarios, and it is illustrated with two applications.