Nonseparable, Stationary Covariance Functions for Space–Time Data

Abstract

Geostatistical approaches to spatiotemporal prediction in environmental science, climatology, meteorology, and related fields rely on appropriate covariance models. This article proposes general classes of nonseparable, stationary covariance functions for spatiotemporal random processes. The constructions are directly in the space–time domain and do not depend on closed-form Fourier inversions. The model parameters can be associated with the data's spatial and temporal structures, respectively; and a covariance model with a readily interpretable space–time interaction parameter is fitted to wind data from Ireland.