An information criterion for detecting periodicities in functional time series

2026-03-22

AI Summary

This study addresses the challenge of identifying an unknown number of periodic components in functional time series by proposing a novel information criterion with theoretical consistency guarantees. The method integrates least squares fitting with residual process analysis and employs an iterative strategy to adaptively estimate the number of periodicities, making it applicable to a broad class of functional time series models. Extensive numerical simulations demonstrate that the proposed criterion performs exceptionally well in finite samples. Furthermore, its practical utility and effectiveness are corroborated through real-data applications to temperature and sunspot records, where it successfully uncovers statistically significant periodic structures.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Reasoning under Uncertainty: Relational Probabilistic Models
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience

Abstract

We propose an information criterion for determining an unknown number of periodic components in functional time series. Identifying the number of frequencies in large-scale time series has been a central focus. To achieve this goal, we suggest an iterative procedure, utilizing the residual process obtained through least squares fitting. This iterative approach demonstrates broad applicability. We establish the consistency of the estimated number of periodic components by minimizing the information criterion. The efficacy of the procedure is illustrated through numerical simulations. In real data analysis, we apply this information criterion to temperature data and sunspot data.

Problem

• functional time series
• periodicity detection
• number of frequencies
• information criterion

Innovation

• information criterion
• functional time series
• periodicity detection
• iterative procedure
• consistency