Journal ArticleDOI
Improved Surrogate Data for Nonlinearity Tests.
Thomas Schreiber,Andreas Schmitz +1 more
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TLDR
It is shown that nonlinear rescalings of a Gaussian linear stochastic process cannot be accounted for by a simple amplitude adjustment of the surrogates which leads to spurious detection of nonlinearity.Abstract:
Current tests for nonlinearity compare a time series to the null hypothesis of a Gaussian linear stochastic process. For this restricted null assumption, random surrogates can be constructed which are constrained by the linear properties of the data. We propose a more general null hypothesis allowing for nonlinear rescalings of a Gaussian linear process. We show that such rescalings cannot be accounted for by a simple amplitude adjustment of the surrogates which leads to spurious detection of nonlinearity. An iterative algorithm is proposed to make appropriate surrogates which have the same autocorrelations as the data and the same probability distribution.read more
Citations
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Measure profile surrogates: A method to validate the performance of epileptic seizure prediction algorithms
Thomas Kreuz,Thomas Kreuz,Ralph G. Andrzejak,Florian Mormann,Alexander Kraskov,Harald Stögbauer,Christian E. Elger,Klaus Lehnertz,Peter Grassberger +8 more
TL;DR: A method to statistically validate the performance of measures used to predict epileptic seizures by applying two measures of synchronization to a quasicontinuous EEG recording and by evaluating their predictive performance using a straightforward seizure prediction statistics.
Journal ArticleDOI
Bubble Entropy: An Entropy Almost Free of Parameters
TL;DR: A new definition of entropy aiming to reduce the significance of this selection is proposed, based on permutation entropy, which presents remarkable stability and exhibits increased descriptive and discriminating power compared to all other definitions, including the most popular ones.
Journal ArticleDOI
Demonstration of nonlinear components in heart rate variability of healthy persons
Christian Braun,Peter Kowallik,Ansgar Freking,Dörte Hadeler,Klaus-Dietrich Kniffki,Malte Meesmann +5 more
TL;DR: R-R intervals from healthy persons contain more information than can be extracted by linear analysis in the time and frequency domain, and time irreversibility of the heartbeat data is demonstrated.
Journal ArticleDOI
Quantification of Long-Range Persistence in Geophysical Time Series: Conventional and Benchmark-Based Improvement Techniques
Annette Witt,Bruce D. Malamud +1 more
TL;DR: In this paper, the authors compare rescaled range (R/S) analysis, semivariogram analysis, detrended fluctuation analysis, and power spectral analysis for quantifying self-affine long-range persistence.
Journal ArticleDOI
Establishing the stochastic nature of intracellular calcium oscillations from experimental data
TL;DR: Analytical analyses provide strong evidence that the measured calcium traces in hepatocytes are prevalently of stochastic nature, and the biological importance of this finding is discussed in relation to the mechanisms incorporated in mathematical models as well as the role of stoChasticity and determinism at cellular and tissue levels.
References
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Book
Time Series Prediction: Forecasting The Future And Understanding The Past
TL;DR: By reading time series prediction forecasting the future and understanding the past, you can take more advantages with limited budget.
Book
Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence
TL;DR: In this paper, the changing structure of stock returns nonlinearity in foreign exchange summary, relation to other work, and future horizons are discussed, as well as the size and distribution of the BDS statistic quantiles.
Journal ArticleDOI
Constrained-realization Monte-Carlo method for hypothesis testing
TL;DR: The typical-realization approach, on the other hand, does not share this requirement, and can provide an accurate and powerful test without having to sacrifice flexibility in the choice of discriminating statistic, and is found to depend on whether or not the discriminating statistic is pivotal.