Journal ArticleDOI
Improved Surrogate Data for Nonlinearity Tests.
Thomas Schreiber,Andreas Schmitz +1 more
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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
Instantaneous Cardiac Baroreflex Sensitivity: xBRS Method Quantifies Heart Rate Blood Pressure Variability Ratio at Rest and During Slow Breathing
Niels Wessel,Andrej Gapelyuk,Jonas Weiß,Martin Schmidt,Jan F. Kraemer,Karsten Berg,Hagen Malberg,Holger Stepan,Jürgen Kurths,Jürgen Kurths,Jürgen Kurths +10 more
TL;DR: The xBRS method has a potentially large bias in characterizing the capacity of the arterial baroreflex under resting conditions, and is exclusively dominated by the heart rate to systolic blood pressure ratio.
Journal ArticleDOI
Visualization of the controller states of an autogenous mill from time series data
TL;DR: In this paper, the operational variables of an industrial autogenous mill were embedded in a low-dimensional phase space to facilitate visualization of the dynamic behavior of the mill by using a multivariate extension of the method of delay coordinates used in nonlinear time series analysis.
Journal ArticleDOI
Detecting nonlinear dynamics using BDS test and surrogate data in financial time series
TL;DR: The Whitney immersion theorem ideas are presented and generalization of Sauer for fractal sets to rebuild the asymptotic behavior of the phenomena and to investigate evidence of nonlinear dynamics in the reproduced dynamics using the Brock, Dechert, Scheinkman test (BDS).
Posted ContentDOI
Multifractal signatures of perceptual processing on anatomical sleeves of the human body
TL;DR: The results suggest that the accuracy of perception via dynamic touch hinges on specific flowing patterns of multifractal fluctuations that people wear on their anatomical sleeves, and that these patterns influence the information available to mechanoreceptors.
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.