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.

Caponera, A. (2021). SPHARMA approximations for stationary functional time series on the sphere. STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES, 24(3), 609-634 [10.1007/s11203-021-09244-6].

SPHARMA approximations for stationary functional time series on the sphere

Caponera, A
2021

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.
Articolo in rivista - Articolo scientifico
Time-varying spherical random fields; Functional time series; Double spectral representation; Spherical harmonics; Spherical functional ARMA
English
2021
24
3
609
634
none
Caponera, A. (2021). SPHARMA approximations for stationary functional time series on the sphere. STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES, 24(3), 609-634 [10.1007/s11203-021-09244-6].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/410983
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