Change Point Detection for Functional Autoregressive Processes on the Sphere

2025-12-02

AI Summary

This paper addresses the problem of detecting structural change points in spherical functional autoregressive (SPHAR) processes. We propose a nonparametric change-point detection method that integrates penalized dynamic programming with LASSO regularization directly in the spherical harmonic domain, jointly modeling spatiotemporal dependence and sparse change structures without requiring prior knowledge of the number or locations of change points. To our knowledge, this is the first work to combine LASSO regularization with spherical harmonic analysis for change-point inference in spherical functional time series, and we establish a theoretical framework with finite-sample consistency guarantees. Empirical results demonstrate that the method achieves high detection accuracy even when the true number of change points is unknown, significantly improving the modeling and diagnostic capability for nonstationarity in spherical spatiotemporal fields—such as climate data and cosmic microwave background radiation—and provides a novel paradigm for statistical inference on high-dimensional spherical data.

Technology Category

• Machine Learning: Kernel Methods
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Detects structural breaks in spherical functional autoregressive processes
• Identifies change points in spatio-temporal fields without prior knowledge
• Analyzes nonstationary phenomena on the sphere for climate and cosmology

Innovation

• LASSO-regularized estimator for spherical functional autoregressive processes
• Penalized dynamic programming in the harmonic domain
• Non-asymptotic theoretical guarantees without prior change point knowledge