Classes of Nonseparable, Spatio-Temporal Stationary Covariance Functions

Abstract

Suppose that a random process Z(s;t), indexed in space and time, has spatio-temporal stationary covariance C(h;u), where h ∈ ℝ_d (d ≥ 1) is a spatial lag and u ∈ ℝ is a temporal lag. Separable spatio-temporal covariances have the property that they can be written as a product of a purely spatial covariance and a purely temporal covariance. Their ease of definition is counterbalanced by the rather limited class of random processes to which they correspond. In this article we derive a new approach that allows one to obtain many classes of nonseparable, spatio-temporal stationary covariance functions and fit several such classes to spatio-temporal data on wind speed over a region in the tropical western Pacific ocean.

Key Words:

• Bochner's theorem
• Matern covariance
• Positive definite
• Simple kriging.