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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Dynamic Behavior of Buoyancy-Induced Flame Oscillation Under Swirling Flow by a Use of Nonlinear Time Series Analysis in Combination with Surrogate Data Method
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A Two-Layered Diffusion Model Traces the Dynamics of Information Processing in the Valuation-and-Choice Circuit of Decision Making
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Chaos and complexity in mine grade distribution series detected by nonlinear approaches
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Proceedings ArticleDOI
Testing for nonlinearity in non-stationary physiological time series
TL;DR: This document proposes a methodology to extend the procedure for generating constrained surrogate time series in order to assess nonlinearity in non-stationary data based on the band-phase-randomized surrogates, which consists in randomizing only a portion of the Fourier phases in the high frequency domain.
Journal ArticleDOI
Warped phase coherence: An empirical synchronization measure combining phase and amplitude information.
TL;DR: In this article, the authors demonstrate that adding a possibly complex constant value to this normally null-mean signal has a non-trivial warping effect, which introduces a level of sensitivity to the amplitude fluctuations and average relative phase.
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.