SPHARMA approximations for stationary functional time series on the sphere
Statistics Theory
2020-09-29 v1 Probability
Statistics Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2009.13189,
title = {SPHARMA approximations for stationary functional time series on the sphere},
author = {Alessia Caponera},
journal= {arXiv preprint arXiv:2009.13189},
year = {2020}
}