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.

翻译：我们提出了一种用于球面函数自回归过程变点检测的新框架，能够识别球面上时空随机场的结构突变。基于谐波域中惩罚动态规划的LASSO正则化估计器，无需预先知晓变点的数量或位置，并提供非渐近的理论保证。该方法为分析球面上的非平稳现象提供了新工具，适用于气候科学、宇宙学等领域。