18 - Statistical Analysis of Spatio-Temporal Models and Their Applications

Abstract

Abstract In this chapter, we briefly review existing literature on Kriging of spatial random processes. In order to define a nonlinear type of Kriging estimator, we introduce measures of nonlinear dependence from the point of view of Kriging. Although we propose a methodology for testing, the distribution theory of the test statistics need to be investigated. We consider spatio-temporal processes at several locations and defining discrete Fourier transforms taken over the time series data at each location, we define simultaneous autoregressive spatio-temporal autoregressive (SAST) models and conditional spatio-temporal autoregressive models (CAST) in terms of these complex-valued random processes. These are similar to simultaneous autoregressive models of Whittle (Whittle, P., 1954. On stationary processes in the plane. Biometrika 49, 305–314) and conditional autoregressive models considered by Bartlett (Bartlett, M.S., 1978. Nearest neighbour models in the analysis of field experiments. J. R. Stat. Soc. Ser. B 40, 147–174) and Besag (Besag, J., 1974. Spatial interaction and the statistical analysis of lattice systems. J. R. Stat. Soc. Ser. B 36, 192–225). We outline an approach for the estimation of the models. We describe recent results by the authors and their co-authors on Space–time autoregressive models.