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SPHARMA approximations for stationary functional time series on the sphere

Author

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  • Alessia Caponera

    (Università di Roma Tor Vergata
    Ecole Polytechnique Fédérale de Lausanne)

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.

Suggested Citation

  • Alessia Caponera, 2021. "SPHARMA approximations for stationary functional time series on the sphere," Statistical Inference for Stochastic Processes, Springer, vol. 24(3), pages 609-634, October.
    • Handle: RePEc:spr:sistpr:v:24:y:2021:i:3:d:10.1007_s11203-021-09244-6
    DOI: 10.1007/s11203-021-09244-6
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    References listed on IDEAS

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