SPHARMA approximations for stationary functional time series on the sphere

2020/09/28 by Caponera, Alessia · 2 citations
#60F05 #60G15 #60G60 #62M40 #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST) #primary 62M15 #secondary 62M10

paper · doi:10.48550/arxiv.2009.13189

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.

Cited by

• Change Point Detection for Functional Autoregressive Processes on the Sphere
• Fractional Cointegration of Geometric Functionals

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