Statistics Colloquium : Dr. Pramita Bagchi

Title: Adaptive frequency band analysis for nonstationary functional time series

Abstract: The frequency-domain properties of nonstationary functional time series often contain valuable information. These properties are characterized through its time-varying power spectrum, which describes the contribution to the variability of a functional time series from waveforms oscillating at different frequencies over time. Practitioners seeking low-dimensional summary measures of the power spectrum often partition frequencies into bands and create collapsed measures of power within these bands. However, standard frequency bands have largely been developed through subjective inspection of time series data and may not provide adequate summary measures of the power spectrum. In this work, we provide an adaptive frequency band estimation for nonstationary functional time series that adequately summarizes the time-varying dynamics of the series and simultaneously accounts for the complex interaction between the functional and temporal dependence structures. We develop scan statistics that takes a high value around any change in the frequency domain. We establish the theoretical properties of this statistic and develop a computationally efficient scalable algorithm to implement it. The validity of our method is also justified through numerous simulation studies and application to EEG data.