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 pro-
cedure for estimation and prediction of linear time processes exhibiting both short-
and long-range dependence and a spatial dependence structure given on the loca-
tions. 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.

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