Paper Info
Title
Detecting determinism in short time series, with an application to the analysis of a stationary EEG recording.
Abstract
We have developed a new method for detecting determinism in a short time series and used this method to examine whether a stationary EEG is deterministic or stochastic. The method is based on the observation that the trajectory of a time series generated from a differentiable dynamical system behaves smoothly in an embedded phase space. The angles between two successive directional vectors in the trajectory reconstructed from a time series at a minimum embedding dimension were calculated as a function of time. We measured the irregularity of the angle variations obtained from the time series using second-order difference plots and central tendency measures, and compared these values with those from surrogate data. The ability of the proposed method to distinguish between chaotic and stochastic dynamics is demonstrated through a number of simulated time series, including data from Lorenz, Rössler, and Van der Pol attractors, high-dimensional equations, and 1/f noise. We then applied this method to the analysis of stationary segments of EEG recordings consisting of 750 data points (6-s segments) from five normal subjects. The stationary EEG segments were not found to exhibit deterministic components. This method can be used to analyze determinism in short time series, such as those from physiological recordings, that can be modeled using differentiable dynamical processes.
Year
DOI
Venue
2002
10.1007/s00422-001-0299-5
Biological Cybernetics
Keywords
Field
DocType
Time Series,Stochastic Dynamic,Surrogate Data,Deterministic Component,Difference Plot
Attractor,Order of integration,Cross-spectrum,Van der Pol oscillator,Differentiable function,Artificial intelligence,Surrogate data,Dynamical system,Mathematics,Trajectory,Machine learning
Journal
Volume
Issue
ISSN
86
5
0340-1200
Citations 
PageRank 
References 
3
0.77
2
Authors
3
Name
Order
Citations
PageRank
Jaeseung Jeong19517.93
John C Gore261641.36
Bradley S Peterson311516.96