Learning dynamics from nonstationary time series: analysis of electroencephalograms.

Abstract

We propose an empirical modeling technique for a nonstationary time series analysis. Proposed methods include a high-dimensional (N>3) dynamical model construction in the form of delay differential equations, a nonparametric method of respective time delay calculation, the detection of quasistationary regions of the process by recurrence analysis in the space of model coefficients, and final fitting of the model to quasistationary segments of observed time series. We also demonstrate the effectiveness of our approach for nonstationary signal classification in the space of model coefficients. Applying the empirical modeling technique to electroencephalogram (EEG) records analysis, we find evidence of high-dimensional nonlinear dynamics in quasistationary EEG segments. Recurrence analysis of model parameters reveals long-term correlations in nonstationary EEG records. Using the dynamical model as a nonlinear filter, we find that different emotional states of subjects can be clearly distinguished in the space of model coefficients.