Multivariate Asymmetric Spatial Covariance with Confluent Hypergeometric Marginals

We introduce a multivariate asymmetric spatial covariance model that replaces Matérn marginals with confluent hypergeometric (CH) covariance functions, providing greater flexibility in smoothness and tail behavior. Environmental processes often exhibit spatial delays, especially under the influence of prevailing wind or water flows, resulting in asymmetric cross-covariances between variables. Our construction operates within the conditional framework of Cressie and Zammit-Mangion (2016), using interaction functions to encode asymmetric cross-variable dependence. We give sufficient conditions on a class of interaction functions under which the resulting CH-based multivariate covariance is positive definite. We evaluate performance through simulation with cokriging, comparing predictive accuracy against multivariate symmetric and asymmetric Matérn-based models and a univariate CH model. We also illustrate the approach with a temperature and pressure dataset, showing improved fit and spatial prediction relative to Matérn-based alternatives.

Spatial statistics

Multivariate spatial statistics

Asymmetric cross-covariance

Confluent hypergeometric covariance

Long-range dependence

Conditional approach 

Section on Statistics and the Environment