Improvements to surrogate data methods for nonstationary time series

Lucio, J.H.; Valdés, R.; Rodríguez, Luis Rouco

doi:10.1103/physreve.85.056202

Cited by 52 publications

(34 citation statements)

References 26 publications

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“…In order to make the results more reliable, particularly in the case of nonstationary EEG signals, we also use the truncated Fourier transform (TFT) surrogates proposed by Nakamura et al [35]. TFT surrogates are particularly useful in preserving some nonstationarity present in the original data in the surrogates, unlike the iAAFT surrogates which can only preserve the linear properties [35,36]. Particularly, we test for randomness based on network measures, the average clustering coefficient C, assortativity R, the average path length L, and the average betweenness centrality BC and independence based on crossnetwork measure, the average cross-clustering coefficient C cross in the focal and nonfocal EEG signals.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of intracranial electroencephalographic recordings from epilepsy patients using univariate and bivariate recurrence networks

Subramaniyam

Hyttinen

2015

Phys. Rev. E

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Recently Andrezejak et al. combined the randomness and nonlinear independence test with iterative amplitude adjusted Fourier transform (iAAFT) surrogates to distinguish between the dynamics of seizure-free intracranial electroencephalographic (EEG) signals recorded from epileptogenic (focal) and nonepileptogenic (nonfocal) brain areas of epileptic patients. However, stationarity is a part of the null hypothesis for iAAFT surrogates and thus nonstationarity can violate the null hypothesis. In this work we first propose the application of the randomness and nonlinear independence test based on recurrence network measures to distinguish between the dynamics of focal and nonfocal EEG signals. Furthermore, we combine these tests with both iAAFT and truncated Fourier transform (TFT) surrogate methods, which also preserves the nonstationarity of the original data in the surrogates along with its linear structure. Our results indicate that focal EEG signals exhibit an increased degree of structural complexity and interdependency compared to nonfocal EEG signals. In general, we find higher rejections for randomness and nonlinear independence tests for focal EEG signals compared to nonfocal EEG signals. In particular, the univariate recurrence network measures, the average clustering coefficient C and assortativity R, and the bivariate recurrence network measure, the average cross-clustering coefficient C(cross), can successfully distinguish between the focal and nonfocal EEG signals, even when the analysis is restricted to nonstationary signals, irrespective of the type of surrogates used. On the other hand, we find that the univariate recurrence network measures, the average path length L, and the average betweenness centrality BC fail to distinguish between the focal and nonfocal EEG signals when iAAFT surrogates are used. However, these two measures can distinguish between focal and nonfocal EEG signals when TFT surrogates are used for nonstationary signals. We also report an improvement in the performance of nonlinear prediction error N and nonlinear interdependence measure L used by Andrezejak et al., when TFT surrogates are used for nonstationary EEG signals. We also find that the outcome of the nonlinear independence test based on the average cross-clustering coefficient C(cross) is independent of the outcome of the randomness test based on the average clustering coefficient C. Thus, the univariate and bivariate recurrence network measures provide independent information regarding the dynamics of the focal and nonfocal EEG signals. In conclusion, recurrence network analysis combined with nonstationary surrogates can be applied to derive reliable biomarkers to distinguish between epileptogenic and nonepileptogenic brain areas using EEG signals.

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Section: Introductionmentioning

confidence: 99%

Dynamics of intracranial electroencephalographic recordings from epilepsy patients using univariate and bivariate recurrence networks

Subramaniyam

Hyttinen

2015

Phys. Rev. E

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“…Besides that, in this work, we are interested in analyzing the advantages of using decomposition methods to produce surrogate data regardless of the presence of nonstationary behavior. A comparative study among those methods can be found in [Maiwald et al, 2008;Schreiber & Schmitz, 1996;Lucio et al, 2012].…”

Section: Surrogate Methodsmentioning

confidence: 99%

“…The TFTS method was later considered by Lucio et al [2012], who presented two new techniques named AAFT TD and IAAFT TD . Similarly to our approach, the authors designed these techniques to preserve the global nonstationarity present in time series.…”

Section: Surrogate Methodsmentioning

confidence: 99%

“…The drawback of the AAFT method is that surrogates are produced respecting the same amplitude distribution of the original time series and presenting similar ACF, but not equal, once there is an adjustment on the amplitude [Theiler et al, 1992;Lucio et al, 2012]. Aiming at improving AAFT to produce surrogates that preserve both amplitude distribution and ACF, Schreiber and Schmitz [1996] proposed a new method called Iterative Amplitude Adjusted Fourier Transformed (IAAFT).…”

Section: Surrogate Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Testing for Linear and Nonlinear Gaussian Processes in Nonstationary Time Series

Rios

Small

Mello

2015

Int. J. Bifurcation Chaos

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Surrogate data methods have been widely applied to produce synthetic data, while maintaining the same statistical properties as the original. By using such methods, one can analyze certain properties of time series. In this context, Theiler's surrogate data methods are the most commonly considered approaches. These are based on the Fourier transform, limiting them to be applied only on stationary time series. Consequently, time series including nonstationary behavior, such as trend, produces spurious high frequencies with Theiler's methods, resulting in inconsistent surrogates. To solve this problem, we present two new methods that combine time series decomposition techniques and surrogate data methods. These new methods initially decompose time series into a set of monocomponents and the trend. Afterwards, traditional surrogate methods are applied on those individual monocomponents and a set of surrogates is obtained. Finally, all individual surrogates plus the trend signal are combined in order to create a single surrogate series. Using this method, one can investigate linear and nonlinear Gaussian processes in time series, irrespective of the presence of nonstationary behavior.

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“…An improved version of the AAFT algorithm has been suggested by Schreiber and Schmitz [8,9] using an iterative scheme called the IAAFT surrogates, which is reported to be more consistent to test null hypothesis [7]. Recently, Nakamura et al [10] have proposed a surrogate generation method called Truncated Fourier Transform (TFT) [11]. However, the surrogate data generated by this method are influenced by a cut-off frequency.…”

Section: Introductionmentioning

confidence: 99%

Recurrence network measures for hypothesis testing using surrogate data: Application to black hole light curves

Jacob

Harikrishnan

Misra

et al. 2018

Communications in Nonlinear Science and Numerical Simulation

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Recurrence networks and the associated statistical measures have become important tools in the analysis of time series data. In this work, we test how effective the recurrence network measures are in analyzing real world data involving two main types of noise, white noise and colored noise. We use two prominent network measures as discriminating statistic for hypothesis testing using surrogate data for a specific null hypothesis that the data is derived from a linear stochastic process. We show that the characteristic path length is especially efficient as a discriminating measure with the conclusions reasonably accurate even with limited number of data points in the time series. We also highlight an additional advantage of the network approach in identifying the dimensionality of the system underlying the time series through a convergence measure derived from the probability distribution of the local clustering coefficients. As examples of real world data, we use the light curves from a prominent black hole system and show that a combined analysis using three primary network measures can provide vital information regarding the nature of temporal variability of light curves from different spectroscopic classes.

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Improvements to surrogate data methods for nonstationary time series

Cited by 52 publications

References 26 publications

Dynamics of intracranial electroencephalographic recordings from epilepsy patients using univariate and bivariate recurrence networks

Dynamics of intracranial electroencephalographic recordings from epilepsy patients using univariate and bivariate recurrence networks

Testing for Linear and Nonlinear Gaussian Processes in Nonstationary Time Series

Recurrence network measures for hypothesis testing using surrogate data: Application to black hole light curves

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