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By focusing attention on close returns of a trajectory to itself, the existence of deterministic dynamics underlying a time series can be detected even in very short data sets. This provides a practical means of detecting determinism in moderate-dimensional (e.g. 7) noisy systems, or low-dimensional systems with large Lyapunov exponents such as computer(More)
  • William A Barnett, A Ronald Gallant, Melvin J Hinich, Daniel T Kaplan, Mark J Jensen
  • 1997
Interest has been growing in testing for nonlinearity or chaos in economic data, but much controversy has arisen about the available results. This paper explores the reasons for these empirical difficulties. We designed and ran a single-blind controlled competition among five highly regarded tests for nonlinearity or chaos with ten simulated data series.(More)
We use a Monte-Carlo approach to investigate the performance of ve diierent time-series estimators of the exponent in 1=f noise. We nd that a maximum-likelihood estimator is markedly superior to Fourier regression methods and Hurst exponent methods. The results indicate that useful estimates of can be made from time series that are much shorter than(More)
Entropy measurement can discriminate among complex systems, including deterministic, stochastic and composite systems. We evaluated the changes of approximate entropy (ApEn) in signals of the electroencephalogram (EEG) during sleep. EEG signals were recorded from eight healthy volunteers during nightly sleep. We estimated the values of ApEn in EEG signals(More)
STUDY OBJECTIVE The breath-to-breath variability of respiratory parameters changes with sleep stage. This study investigates any alteration in the approximate entropy (ApEn) of respiratory movement as a gauge of complexity in respiration, by stage of consciousness, in the light of putative brain interactions. PARTICIPANTS Eight healthy men, who were(More)
The electrical activity of the heart usually shows dynamical behavior which is neither periodic nor deterministically chaotic: The interbeat intervals seem to contain a random component. Although long term predictions are thus impossible, good predictions can be made for times smaller than one heart cycle. This fact is used in order to suppress measurement(More)
For several decades, a number of methods have been developed for the noninvasive assessment of the level of consciousness during general anesthesia. In this paper, detrended fluctuation analysis is used to study the scaling behavior of the electroencephalogram as a measure of the level of consciousness. Three indexes are proposed in order to characterize(More)
Many techniques for time series analysis are based on the idea of representing the time series z 1 ,. .. , z N as a probability density. For example, the correlation and information dimensions can be written in terms of an integral over a probability density p(z t , z t−h ,. .. , z t−(m−1)h) in a lag embedding space [1] of dimension m and lag h ; the mutual(More)
The approximate entropy (ApEn) of signals in the electroencephalogram (EEG) was evaluated in 8 healthy volunteers and in 10 patients with absence epilepsy, both during seizure-free and seizure intervals. We estimated the nonlinearity of each 3-sec EEG segment using surrogate data methods. The mean (+/- SD) ApEn in EEG was 0.83 +/- 0.22 in healthy subjects(More)
We describe a method to suppress maternal and noise contaminations in single-lead fetal ECG recordings. A nonlinear state space projection technique originally developed for noise reduction in deterministically chaotic signals is used. The method is successfully applied to recordings with fetal components and noise of comparable amplitude.