A Comparative Study of Some Stochastic Methods and Autoprojective Models for Spatial Processes

Abstract

Spatial stochastic processes often show a distinct persistence, which becomes noticeable in a nonrandom spatial grouping of similar or regularly dissimilar values. Various methods have been developed for statistically analyzing such persistence effects which are dependent upon distance and direction. Important differences and similarities in the concept of spatial autocorrelation and the theory of regionalized variables will be pointed out and explained by means of examples. The use of these geostatistical methods in modelling spatial processes leads to the SAR (spatial auto-regressive) models and to the Kriging concept, respectively. Although SAR models are used in particular to represent spatial persistences as characteristic endogenous dependency structures, the Kriging method is more pragmatically orientated to the interpolation and extrapolation of spatial data. The suitability of such stochastic models in purely spatial forecasting and also in the estimation of areal means will be described by use of examples, and compared with conventional methods.