Nonseparable Space-Time Covariance Models: Some Parametric Families

By extending the product and product–sum space-time covariance models, new families are generated as integrated products and product–sums. These include nonintegrable space-time covariance models not obtainable by the Cressie–Huang representation. It is shown how to fit the spatial and temporal components of the models as well as the probability density function. The methods are illustrated by a case study.

[1]  Wei-Liem Loh,et al.  Estimating structured correlation matrices in smooth Gaussian random field models , 2000 .

[2]  Phaedon C. Kyriakidis,et al.  Geostatistical Space–Time Models: A Review , 1999 .

[3]  S. De Iacoa,et al.  Space – time analysis using a general product – sum model , 2000 .

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

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

[6]  G. Christakos On the Problem of Permissible Covariance and Variogram Models , 1984 .

[7]  I. Rodríguez‐Iturbe,et al.  The design of rainfall networks in time and space , 1974 .

[8]  George Christakos,et al.  Random Field Models in Earth Sciences , 1992 .

[9]  D. Myers,et al.  Space–time analysis using a general product–sum model , 2001 .

[10]  G. Matheron The intrinsic random functions and their applications , 1973, Advances in Applied Probability.

[11]  Noel A Cressie,et al.  Statistics for Spatial Data. , 1992 .

[12]  Shahrokh Rouhani,et al.  Space-Time Kriging of Groundwater Data , 1989 .

[13]  D. F. Hays,et al.  Table of Integrals, Series, and Products , 1966 .

[14]  D. Myers,et al.  Problems in space-time kriging of geohydrological data , 1990 .

[15]  Jean-Paul Chilbs,et al.  Geostatistics , 2000, Technometrics.

[16]  D. Myers,et al.  Estimating and modeling space–time correlation structures , 2001 .

[17]  Donato Posa,et al.  Spatial-Temporal Modeling of SO2 in Milan District , 1997 .

[18]  Donato Posa,et al.  Product‐sum covariance for space‐time modeling: an environmental application , 2001 .

[19]  D. Myers,et al.  Variograms with zonal anisotropies and noninvertible kriging systems , 1990 .

[20]  Donato Posa,et al.  A simple description of spatial-temporal processes , 1993 .

[21]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[22]  Donald E. Myers,et al.  INTERPOLATION WITH POSITIVE DEFINITE FUNCTIONS , 1988 .

[23]  Richard A. Davis,et al.  Time Series: Theory and Methods , 2013 .