Dynamic Bayesian Multitaper Spectral Analysis

Abstract

Nonparametric spectral analysis using overlapping sliding windows is among the most widely used techniques in analyzing nonstationary time series. Although sliding window analysis is convenient to implement, the resulting estimates are sensitive to the window length and overlap size. In addition, it undermines the dynamics of the time series as the estimate at each window uses only the data within. Finally, estimates from overlapping windows hinder a precise statistical assessment of the estimates. In this paper, we address these shortcomings by explicitly modeling and estimating the spectral dynamics through integrating the multitaper method with state-space models in a Bayesian estimation framework. We propose two spectral estimators that are able to capture spectral dynamics at high spectrotemporal resolution. We provide theoretical analysis of the bias-variance trade-offs, which establish performance gains over the multitaper method. We apply our algorithms to synthetic data as well as real data from human EEG and electric network frequency recordings, which corroborate our theoretical analysis.