Topic
Surrogate data testing
About: Surrogate data testing is a research topic. Over the lifetime, 39 publications have been published within this topic receiving 10210 citations.
Papers
TL;DR: The issue of determining an acceptable minimum embedding dimension is examined by looking at the behavior of near neighbors under changes in the embedding dimensions from d\ensuremath{\rightarrow}d+1 by examining the manner in which noise changes the determination of ${\mathit{d}}_{\math it{E}}$.
Abstract: We examine the issue of determining an acceptable minimum embedding dimension by looking at the behavior of near neighbors under changes in the embedding dimension from d\ensuremath{\rightarrow}d+1. When the number of nearest neighbors arising through projection is zero in dimension ${\mathit{d}}_{\mathit{E}}$, the attractor has been unfolded in this dimension. The precise determination of ${\mathit{d}}_{\mathit{E}}$ is clouded by ``noise,'' and we examine the manner in which noise changes the determination of ${\mathit{d}}_{\mathit{E}}$. Our criterion also indicates the error one makes by choosing an embedding dimension smaller than ${\mathit{d}}_{\mathit{E}}$. This knowledge may be useful in the practical analysis of observed time series.
3,893 citations
TL;DR: In this article, a statistical approach for identifying nonlinearity in time series is described, which first specifies some linear process as a null hypothesis, then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate sets.
3,890 citations
TL;DR: Specific as well as more general approaches to constrained randomisation, providing a full range of examples, and some implementational aspects of the realisation of these methods in the TISEAN software package are discussed.
1,685 citations
TL;DR: 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.
1,571 citations
TL;DR: A detailed overview of a wide range of surrogate types is provided, which include Fourier transform based surrogates, which have since been developed to test increasingly varied null hypotheses while characterizing the dynamics of complex systems, including uncorrelated and correlated noise, coupling between systems, and synchronization.
385 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2019 | 1 |
| 2018 | 2 |
| 2016 | 1 |
| 2015 | 1 |
| 2014 | 1 |
| 2012 | 1 |