Title: Oscillator decomposition of time series data
Takeru Matsuda, Graduate School of Information Science and Technology, The University of Tokyo
Many time series are naturally considered as a superposition of several oscillation components. For example, electroencephalogram (EEG) time series include oscillation components such as alpha, beta, and gamma. We develop a method for decomposing time series data (both univariate and multivariate) into oscillation components and estimating their phases in a data-driven manner (without band-pass filtering). The proposed method is based on Gaussian linear state space models that describe several oscillators underlying the given time series data. These models are fitted to data by using the empirical Bayes method, and the number of oscillators is determined by the Akaike Information Criterion (AIC). Thus, the proposed method provides a natural decomposition of time series data and enables an investigation of the phase dynamics. Simulation results show that the proposed method succeeds in extracting intermittent oscillations like ripples and detecting the phase reset phenomena. We apply the proposed method to real data from various fields. For example, several neural oscillators are extracted from rat hippocampal LFP data, including two oscillators in theta band.