Change Point Detection for Functional Autoregressive Processes on the Sphere

Abstract

We introduce a novel framework for change point detection in spherical functional autoregressive (SPHAR) processes, enabling the identification of structural breaks in spatio-temporal random fields on the sphere. Our LASSO-regularized estimator, based on penalized dynamic programming in the harmonic domain, operates without knowledge of the number or locations of change points and offers non-asymptotic theoretical guarantees. This approach provides a new tool for analyzing nonstationary phenomena on the sphere, relevant to climate science, cosmology, and beyond.