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Spatio-temporal variograms and covariance models

Part of: Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Chunsheng Ma
Chunsheng Ma*
Affiliation:
Wichita State University
*
∗ Postal address: Department of Mathematics and Statistics, Wichita State University, Wichita, KS 67260-0033, USA. Email address: [email protected]
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Abstract

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Variograms and covariance functions are the fundamental tools for modeling dependent data observed over time, space, or space-time. This paper aims at constructing nonseparable spatio-temporal variograms and covariance models. Special attention is paid to an intrinsically stationary spatio-temporal random field whose covariance function is of Schoenberg-Lévy type. The correlation structure is studied for its increment process and for its partial derivative with respect to the time lag, as well as for the superposition over time of a stationary spatio-temporal random field. As another approach, we investigate the permissibility of the linear combination of certain separable spatio-temporal covariance functions to be a valid covariance, and obtain a subclass of stationary spatio-temporal models isotropic in space.

Keywords

Covarianceintrinsically stationaryisotropicpositive definitepower-law decaySchoenberg-Lévy kernelstationaryvariogram

MSC classification

Primary: 60G12: General second-order processes
Secondary: 60G10: Stationary processes 60G60: Random fields
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 37 , Issue 3 , September 2005 , pp. 706 - 725
Copyright
Copyright © Applied Probability Trust 2005 

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