Spatiotemporal covariance functions for Laplacian ARMA fields in higher dimensions

This paper presents clear formulae of the covariance functions of Laplacian ARMA fields in terms of coefficients and Bessel functions in higher spatial dimensions. Spectral methods are used for the study of spatiotemporal Laplacian ARMA fields in Euclidean spaces and spheres therein with dimension d ≥ 2 d\geq 2 .

Multivariate Gaussian Random Fields over Generalized Product Spaces involving the Hypertorus

The paper deals with multivariate Gaussian random fields defined over generalized product spaces that involve the hypertorus. The assumption of Gaussianity implies the finite dimensional distributions to be completely specified by the covariance functions, being in this case matrix valued mappings.

We start by considering the spectral representations that in turn allow for a characterization of such covariance functions. We then provide some methods for the construction of these matrix valued mappings. Finally, we consider strategies to evade radial symmetry (called isotropy in spatial statistics) and provide representation theorems for such a more general case.

SPHARMA approximations for stationary functional time series on the sphere

In this paper, we focus on isotropic and stationary sphere-cross-time random fields. We first introduce the class of spherical functional autoregressive-moving average processes (SPHARMA), which extend in a natural way the spherical functional autoregressions (SPHAR) recently studied in Caponera and Marinucci (Ann Stat 49(1):346–369, 2021) and Caponera et al. (Stoch Process Appl 137:167–199, 2021); more importantly, we then show that SPHAR and SPHARMA processes of sufficiently large order can be exploited to approximate every isotropic and stationary sphere-cross-time random field, thus generalizing to this infinite-dimensional framework some classical results on real-valued stationary processes. Further characterizations in terms of functional spectral representation theorems and Wold-like decompositions are also established.