2025/10/21 by Jiazhen Xu, Andrew T. A. Wood, Xu, Jiazhen +3 · 1 citation
Computer Science · Physics and Astronomy · #Bayesian Methods and Mixture Models #Complex Network Analysis Techniques #FOS: Computer and information sciences #Methodology (stat.ME) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2510.18247
openalex publication_date 2025/10/21 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
Time-varying non-Euclidean random objects are playing a growing role in modern data analysis, and periodicity is a fundamental characteristic of time-varying data. However, quantifying periodicity in general non-Euclidean random objects remains largely unexplored. In this work, we introduce a novel nonparametric framework for quantifying periodicity in random objects within a general metric space that lacks Euclidean structures. Our approach formulates periodicity estimation as a model selection problem and provides methodologies for period estimation, data-driven tuning parameter selection, and periodic component extraction. Our theoretical contributions include establishing the consistency of period estimation without relying on linearity properties used in the literature for Euclidean data, providing theoretical support for data-driven tuning parameter selection, and deriving uniform convergence results for periodic component estimation. Through extensive simulation studies covering three distinct types of time-varying random objects such as compositional data, networks, and functional data, we showcase the superior accuracy achieved by our approach in periodicity quantification. Finally, we apply our method to various real datasets, including U.S. electricity generation compositions, New York City transportation networks, and Germany's water consumption curves, highlighting its practical relevance in identifying and quantifying meaningful periodic patterns.