  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 [8,
7]; 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.
