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Abstract:
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The problem of constructing valid parametric cross-covariance functions is challenging. We propose a simple methodology, based on latent dimensions and existing covariance models for univariate random fields, to develop flexible, interpretable, and computationally feasible classes of cross-covariance functions in closed form. We focus on spatio-temporal cross-covariance functions that can be nonseparable, anisotropic, and asymmetric. We discuss estimation of these models and perform a small simulation study to demonstrate our approach. We illustrate our methodology on a trivariate spatio-temporal pollution data set from California.
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