A method for determinism in short time series, and its application to stationary EEG

A novel method for detecting determinism in short time series is developed and applied to investigate determinism in stationary electroencephalogram (EEG) recordings. This method is based on the observation that the trajectory of a time series generated from a differentiable dynamical system behaves smoothly in an embedded state space. The angles between two successive tangent vectors in the trajectory reconstructed from the time series is calculated as a function of time. The irregularity of the angle variations obtained from the time series is estimated using second-order difference plots, and compared with that of the corresponding surrogate data. Using this method, we demonstrate that scalp EEG recordings from normal subjects do not exhibit a low-dimensional deterministic structure. This method can be useful for analyzing determinism in short time series, such as those from physiological recordings.