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.

翻译：在分析多元空间数据与单变量时空数据时，学界普遍认识到可能存在不对称依赖性，这可在高斯过程框架下通过采用不对称（分别对应矩阵或时空）协方差函数进行处理。本文引入了一种构建不对称时空协方差的新范式，我们称之为“反射不对称”，其基础是近期提出的多元空间数据模型。我们首先为反射不对称多元空间模型提供了新的理论结果，扩展了其适用性。随后，我们提出了其不对称时空扩展模型，该模型的构建视角与拉格朗日不对称时空协方差模型存在本质差异。新模型参数更少：一个参数同时控制空间与时间边缘协方差，且标准可分离模型是其特例。在模拟研究及对经典爱尔兰风速数据的分析中，这些新模型不仅提升了模型拟合与预测性能，且更易于估计。这些特性表明，该模型在环境数据及其他时空数据的改进分析中具有广泛适用性。