Title: Space-Time Geostatistical Models with both Linear and Seasonal Structures in the Temporal Components,
Abstract: 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.