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arXiv · 2305.01392

Multi-Scale CUSUM Tests for Time Dependent Spherical Random Fields

Alessia Caponera·Domenico Marinucci·Anna Vidotto
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Abstract

This paper investigates the asymptotic behavior of structural break tests in the harmonic domain for time dependent spherical random fields. In particular, we prove a functional central limit theorem result for the fluctuations over time of the sample spherical harmonic coefficients, under the null of isotropy and stationarity; furthermore, we prove consistency of the corresponding CUSUM test, under a broad range of alternatives, including deterministic trend, abrupt change, and a nontrivial power alternative. Our results are then applied to NCEP data on global temperature: our estimates suggest that Climate Change does not simply affect global average temperatures, but also the nature of spatial fluctuations at different scales.

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Alessia Caponera, Domenico Marinucci, Anna Vidotto. 2023-05-02. Multi-Scale CUSUM Tests for Time Dependent Spherical Random Fields. https://arxiv.org/abs/2305.01392

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