Interpretable Frequency Band Summary Measures and Analysis For Multiple Nonstationary Biomedical Time Series

C. Brubaker, R. Lee and S. A. Bruce

Texas A&M University

This work develops a likelihood-based methodology for estimating frequency bands in collections of nonstationary time series that exhibit replicate-specific spectral variability, with a motivating application to pupil diameter dynamics in children with and without attention deficit hyperactivity disorder (ADHD). The proposed framework approximates time-varying spectra using piecewise-smooth functional summaries over data-adaptive frequency bands, where each band-specific trend is modeled via spline bases whose complexity is jointly selected with the number of bands. Model complexity is controlled through a minimum description length (MDL) criterion that balances fit and parsimony, and a genetic algorithm is implemented to efficiently explore the large combinatorial space of band endpoints and spline knot configurations. Simulation studies demonstrate that the procedure accurately recovers frequency band structure and time-varying summaries, with improved performance as the number and length of replicates increase. Applied to pupil diameter time series collected during a visuospatial working memory task, the method identifies physiologically meaningful bands and reveals temporal patterns of spectral power that discriminate ADHD from control subjects, yielding high classification performance when used as input to downstream logistic and tree-based classifiers.

Keywords: Nonstationary time series, Spectral analysis, Biomedical signals.