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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Journal ArticleDOI
The epileptic process as nonlinear deterministic dynamics in a stochastic environment: an evaluation on mesial temporal lobe epilepsy.
Ralph G. Andrzejak,Guido Widman,Klaus Lehnertz,Christoph Rieke,Peter David,Christian E. Elger +5 more
TL;DR: This analysis framework was extended by introducing a new measure xi, designed to discriminate between nonlinear deterministic and linear stochastic dynamics, which allowed to retrospectively determine the side of the epileptogenic zone in full agreement with results of the presurgical workup.
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Low doses of ethanol reduce evidence for nonlinear structure in brain activity.
TL;DR: Findings are consistent with the notion that ethanol may act by introducing a level of randomness in neuronal processing as assessed by EEG nonlinear structure, as evidenced by the measures of time asymmetry, determinism, and redundancy.
Journal ArticleDOI
Dynamics of representational change: entropy, action, and cognition.
TL;DR: Two studies provide an initial test of the hypothesis that the emergence of new cognitive structure follows the same universal principles as emergence in other domains, and show that increasing environmental entropy accelerated discovery, a classic prediction from dynamics.
Journal ArticleDOI
Bivariate surrogate techniques: necessity, strengths, and caveats.
Ralph G. Andrzejak,Alexander Kraskov,Harald Stögbauer,Florian Mormann,Thomas Kreuz,Thomas Kreuz +5 more
TL;DR: This work analyzes eight different stochastic and deterministic models designed to test against a different null hypothesis, e.g., an underlying bivariate linear Stochastic process or nonlinear deterministic process.
Journal ArticleDOI
Twin surrogates to test for complex synchronisation
TL;DR: This technique generates surrogates which correspond to an independent copy of the underlying system which are well suited to test for complex synchronisation and exemplify this for the paradigmatic system of Rossler oscillators.
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.