Adaptive Frequency Band Analysis for Functional Time Series

TL;DR

This paper introduces an adaptive method for estimating frequency bands in nonstationary functional time series, improving the summarization of time-varying spectral properties with theoretical guarantees and practical validation.

Contribution

It proposes a novel framework with a scan statistic and search algorithm for adaptive frequency band detection, addressing limitations of manual band selection.

Findings

Effective detection of frequency changes in simulations

Accurate summarization of EEG data dynamics

Theoretical properties established for the method

Abstract

The frequency-domain properties of nonstationary functional time series often contain valuable information. These properties are characterized through its time-varying power spectrum. Practitioners seeking low-dimensional summary measures of the power spectrum often partition frequencies into bands and create collapsed measures of power within bands. However, standard frequency bands have largely been developed through manual inspection of time series data and may not adequately summarize power spectra. In this article, we propose a framework for adaptive frequency band estimation of nonstationary functional time series that optimally summarizes the time-varying dynamics of the series. We develop a scan statistic and search algorithm to detect changes in the frequency domain. We establish theoretical properties of this framework and develop a computationally-efficient implementation. The validity of our method is also justified through numerous simulation studies and an application to analyzing electroencephalogram data in participants alternating between eyes open and eyes closed conditions.