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Spatially-indexed multivariate data appear frequently in geostatistics andrelated fields including oceanography and environmental science. To take fulladvantage of this data structure, cross-covariance functions are constructed todescribe the dependence between any two component variables at differentspatial locations. Modeling of multivariate spatial random fields requiresthese constructed cross-covariance functions to be valid, which often presentschallenges that lead to complicated restrictions on the parameter space. Thepurpose of this work is to present techniques using multivariate mixtures forestablishing validity that are simultaneously simplified and comprehensive. Inparticular, cross-covariances are constructed for the recently-introducedconfluent hypergeometric (CH) class of covariance functions, which has slow(polynomial) decay in the tails of the covariance that better handles largegaps between observations in comparison with other covariance models. Inaddition, the spectral density of the confluent hypergeometric covariance isestablished and used to construct new valid cross-covariance models. Theapproach leads to valid multivariate cross-covariance models that inherit thedesired marginal properties of the confluent hypergeometric model andoutperform the multivariate Mat\'ern model in out-of-sample prediction underslowly-decaying correlation of the underlying multivariate random field. Themodel captures heavy tail decay and dependence between variables in anoceanography dataset of temperature, salinity and oxygen, as measured byautonomous floats in the Southern Ocean.

Multivariate Confluent Hypergeometric Covariance Functions with Simultaneous Flexibility over Smoothness and Tail Decay