SPHARMA approximations for stationary functional time series on the sphere

Alessia Caponera ()
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Alessia Caponera: Università di Roma Tor Vergata

Statistical Inference for Stochastic Processes, 2021, vol. 24, issue 3, No 4, 609-634

Abstract: 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 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.

Keywords: Time-varying spherical random fields; Functional time series; Double spectral representation; Spherical harmonics; Spherical functional ARMA; 62M15; 62M10; 60G15; 60F05; 62M40; 60G60 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11203-021-09244-6

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