Families of spatio-temporal stationary covariance models

Abstract This paper provides simple methods for constructing new families of spatio-temporal stationary covariance models from purely spatial (or purely temporal) stationary covariance models. As the application of the methods developed, we introduce spatio-temporal stationary covariance models with the Gaussian and related spatial margins, and develop the Heine family and the Whittle–Matern family of spatio-temporal stationary covariance models.

[1]  I. J. Schoenberg,et al.  Metric spaces and positive definite functions , 1938 .

[2]  George Christakos,et al.  Modern Spatiotemporal Geostatistics , 2000 .

[3]  A. Yaglom Correlation Theory of Stationary and Related Random Functions I: Basic Results , 1987 .

[4]  I. J. Schoenberg Metric spaces and completely monotone functions , 1938 .

[5]  J. Chilès,et al.  Geostatistics: Modeling Spatial Uncertainty , 1999 .

[6]  M. Stein,et al.  A Bayesian analysis of kriging , 1993 .

[7]  Richard H. Jones,et al.  Models for Continuous Stationary Space-Time Processes , 1997 .

[8]  Mike Rees,et al.  5. Statistics for Spatial Data , 1993 .

[9]  P. Brown,et al.  Blur‐generated non‐separable space–time models , 2000 .

[10]  V. Heine MODELS FOR TWO-DIMENSIONAL STATIONARY STOCHASTIC PROCESSES , 1955 .

[11]  Roger Woodard,et al.  Interpolation of Spatial Data: Some Theory for Kriging , 1999, Technometrics.

[12]  David R. Cox,et al.  A simple spatial-temporal model of rainfall , 1988, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[13]  P. Whittle ON STATIONARY PROCESSES IN THE PLANE , 1954 .

[14]  N. Cressie,et al.  Classes of nonseparable, spatio-temporal stationary covariance functions , 1999 .

[15]  A. Erdélyi,et al.  Tables of integral transforms , 1955 .

[16]  J. R. Wallis,et al.  An Approach to Statistical Spatial-Temporal Modeling of Meteorological Fields , 1994 .

[17]  P. Whittle,et al.  Topographic correlation, power-law covariance functions, and diffusion , 1962 .