Classes of Nonseparable , Spatio - temporal

Suppose that a random process Z(s; t), indexed in space and time, has a spatio-temporal stationary covariance C(h; u), where h 2 IR d (d 1) is a spatial lag and u 2 IR 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 deenition is counterbalanced by the rather limited class of random processes to which they correspond. In this note, we derive a new approach that allows one to obtain many classes of nonseparable, spatio-temporal stationary covariance functions and we t one such to spatio-temporal data on wind speed over a region in the tropical western Paciic ocean.