An information criterion for detecting periodicities in functional time series

TL;DR

This paper introduces an information criterion and iterative method to accurately identify the number of periodic components in functional time series, demonstrated through simulations and real-world temperature and sunspot data.

Contribution

It presents a novel information criterion and an iterative approach for detecting periodicities in functional time series, with proven consistency and broad applicability.

Findings

Consistent estimation of the number of periodic components.

Effective in large-scale and real-world data.

Validated through numerical simulations and real data analysis.

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.