Caponera, Alessia2021-06-052021-06-052021-06-052021-05-1210.1007/s11203-021-09244-6https://infoscience.epfl.ch/handle/20.500.14299/178536WOS:000652471500001In 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.Statistics & ProbabilityMathematicstime-varying spherical random fieldsfunctional time seriesdouble spectral representationspherical harmonicsspherical functional armacovariance functionsrandom-fieldsmodelstext::journal::journal article::research article