Connecting reflective asymmetries in multivariate spatial and spatio-temporal covariances

TL;DR

This paper introduces a new class of reflective asymmetric covariance functions for multivariate spatial and spatio-temporal data, improving model fit and prediction while simplifying parameter estimation.

Contribution

It extends reflective asymmetric multivariate spatial models to space-time data, offering a novel, less parameter-intensive approach that generalizes separable models.

Findings

Improved model fit and prediction in Irish wind data

Fewer parameters needed for the new models

Models are easier to estimate and broadly applicable

Abstract

In the analysis of multivariate spatial and univariate spatio-temporal data, it is commonly recognized that asymmetric dependence may exist, which can be addressed using an asymmetric (matrix or space-time, respectively) covariance function within a Gaussian process framework. This paper introduces a new paradigm for constructing asymmetric space-time covariances, which we refer to as "reflective asymmetric," by leveraging recently-introduced models for multivariate spatial data. We first provide new results for reflective asymmetric multivariate spatial models that extends their applicability. We then propose their asymmetric space-time extension, which come from a substantially different perspective than Lagrangian asymmetric space-time covariances. There are fewer parameters in the new models, one controls both the spatial and temporal marginal covariances, and the standard separable model is a special case. In simulation studies and analysis of the frequently-studied Irish wind data, these new models also improve model fit and prediction performance, and they can be easier to estimate. These features indicate broad applicability for improved analysis in environmental and other space-time data.