On Hypotheses Testing for the Selection of Spatio-Temporal Models

Several models have been proposed in recent years for analysing spatial data and also, to some extent, spatio-temporal data. One of the important problems, namely the choice of an appropriate model for describing real data sets, remains unsolved. Here we consider the analysis of spatio-temporal processes from which observations over space and time are available. We propose statistical tests for discriminating between space-time autoregressive processes and multivariate autoregressive processes. The sampling properties of the proposed tests are considered. We illustrate the methods with a real example. We use the above tests to find the best model to describe spatio-temporal variations of hourly carbon monoxide measurements at four locations in London in January 2004. Copyright 2006 The Authors Journal compilation 2006 Blackwell Publishing Ltd.