时间分量同时具有线性和季节结构的时空地质统计模型
Space-Time Geostatistical Models with both Linear and Seasonal Structures in the Temporal Components
摘要：
我们提供了一种新的方法来模拟时空随机场的时间参数被分解成两个部分。前者抓住了线性论证，例如，它与场的年度演变有关。后者是一个循环变量，例如，描述每月的观测结果。这种构造背后的基本直觉是考虑在时间上定义在空间（$d$维欧几里得空间的紧致集）上的随机场，其被认为是积空间$\mathbb{R} \times \mathbb{S}^1$，其中$\mathbb{S}^1$是单位圆。在这样的框架下，我们得到新的参数族的协方差函数。特别是，我们专注于两类参数家庭。前者是协方差函数的Gneiting类的括号。而后者是通过提出一个新的拉格朗日框架的空间-时域中考虑的手稿。我们的研究结果通过一个真实的地表气温数据集来说明。我们表明，这两个时间变量的合并可以产生显着的改善模型的预测性能。我们还讨论了这种方法的扩展空间上定义的领域，它允许在大部分的行星地球模型的时空现象。
英文摘要：
We provide a novel approach to model space-time random fields where the temporal argument is decomposed into two parts. The former captures the linear argument, which is related, for instance, to the annual evolution of the field. The latter is instead a circular variable describing, for instance, monthly observations. The basic intuition behind this construction is to consider a random field defined over space (a compact set of the $d$-dimensional Euclidean space) across time, which is considered as the product space $\mathbb{R} \times \mathbb{S}^1$, with $\mathbb{S}^1$ being the unit circle. Under such framework, we derive new parametric families of covariance functions. In particular, we focus on two classes of parametric families. The former being parenthetical to the Gneiting class of covariance functions. The latter is instead obtained by proposing a new Lagrangian framework for the space-time domain considered in the manuscript. Our findings are illustrated through a real dataset of surface air temperatures. We show that the incorporation of both temporal variables can produce significant improvements in the predictive performances of the model. We also discuss the extension of this approach for fields defined spatially on a sphere, which allows to model space-time phenomena over large portions of planet Earth.
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