Detecting Causality from Nonlinear Dynamics with Short-term Time Series

Ma, Huanfei; Aihara, Kazuyuki; Chen, Luonan

doi:10.1038/srep07464

Cited by 91 publications

(90 citation statements)

References 41 publications

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“…precision and sensitivity(or recall, true positive rate) [44, 45]. Precision is defined as Eq (16) and sensitivity is defined as Eq (17).…”

Section: Resultsmentioning

confidence: 99%

Inferring Weighted Directed Association Network from Multivariate Time Series with a Synthetic Method of Partial Symbolic Transfer Entropy Spectrum and Granger Causality

Zhao

2016

PLoS ONE

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Complex network methodology is very useful for complex system explorer. However, the relationships among variables in complex system are usually not clear. Therefore, inferring association networks among variables from their observed data has been a popular research topic. We propose a synthetic method, named small-shuffle partial symbolic transfer entropy spectrum (SSPSTES), for inferring association network from multivariate time series. The method synthesizes surrogate data, partial symbolic transfer entropy (PSTE) and Granger causality. A proper threshold selection is crucial for common correlation identification methods and it is not easy for users. The proposed method can not only identify the strong correlation without selecting a threshold but also has the ability of correlation quantification, direction identification and temporal relation identification. The method can be divided into three layers, i.e. data layer, model layer and network layer. In the model layer, the method identifies all the possible pair-wise correlation. In the network layer, we introduce a filter algorithm to remove the indirect weak correlation and retain strong correlation. Finally, we build a weighted adjacency matrix, the value of each entry representing the correlation level between pair-wise variables, and then get the weighted directed association network. Two numerical simulated data from linear system and nonlinear system are illustrated to show the steps and performance of the proposed approach. The ability of the proposed method is approved by an application finally.

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“…precision and sensitivity(or recall, true positive rate) [44, 45]. Precision is defined as Eq (16) and sensitivity is defined as Eq (17).…”

Section: Resultsmentioning

confidence: 99%

Inferring Weighted Directed Association Network from Multivariate Time Series with a Synthetic Method of Partial Symbolic Transfer Entropy Spectrum and Granger Causality

Zhao

2016

PLoS ONE

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“…For example, tests for the existence of directed unique mappings between reconstructed manifolds can be used as an all or nothing criterion to detect causal links between component systems [6,[11][12][13][14].…”

Section: Discussionmentioning

confidence: 99%

Topological Causality in Dynamical Systems

et al. 2017

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Discovery of causal relations is fundamental for understanding the dynamics of complex systems. While causal interactions are well defined for acyclic systems that can be separated into causally effective subsystems, a mathematical definition of gradual causal interaction is still lacking for nonseparable dynamical systems. The solution proposed here is analytically tractable for time discrete chaotic maps and is shown to fulfill basic requirements for causality measures. It implies a method for determination of directed effective influences using pairs of measurements from dynamical systems. Applications to time series from systems of coupled differential equations and linear stochastic systems demonstrate its general utility.

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“…The detection of causality from a time series is an intensively developing technique (Granger, 1988;Čenys, Lasiene and Pyragas, 1991;Sugihara et al, 2012;Ma, Aihara and Chen, 2014;van Nes et al, 2015) The CD method utilizes one observable (e.g. sunspot area) of an unknown dynamical system (e.g.…”

Section: Causality Detection Methodsmentioning

confidence: 99%

Long-Term Pulses of Dynamic Coupling Between Solar Hemispheres

Volobuev

Makarenko

2017

Sol Phys

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North-south (N-S) asymmetry of solar activity is a known statistical phenomenon but its significance is difficult to prove or theoretically explain. Here we consider each solar hemisphere as a separate dynamical system connected with the other hemisphere via an unknown coupling parameter. We use a non-linear dynamics approach to calculate the scale-dependent conditional dispersion (CD) of sunspots between hemispheres. Using daily Greenwich sunspot areas, we calculated the Neumann and Pearson chi-squared distances between CDs as indices showing the direction of coupling. We introduce an additional index of synchronization which shows the strength of coupling and allows us to discriminate between complete synchronization and independency of hemispheres. All indices are evaluated in a four-year moving window showing the evolution of coupling between hemispheres. We find that the driver-response interrelation changes between hemispheres have a few pulses during 130 years of Greenwich data with an at least 40 years-long period of unidirectional coupling. These sharp nearly simultaneous pulses of all causality indices are found at the decay of some 11-year cycles. The pulse rate of this new phenomenon of dynamic coupling is irregular: although the first two pulses repeat after 22-year Hale cycles, the last two pulses repeat after three and four 11-year cycles respectively. The last pulse occurs at the decay phase of Cycle 23 so the next pulse will likely appear during the decay of future Cycle 25 or later. This new phenomenon of dynamic coupling reveals additional constraints for understanding and modeling of the long-term solar activity cycles.

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Detecting Causality from Nonlinear Dynamics with Short-term Time Series

Cited by 91 publications

References 41 publications

Inferring Weighted Directed Association Network from Multivariate Time Series with a Synthetic Method of Partial Symbolic Transfer Entropy Spectrum and Granger Causality

Inferring Weighted Directed Association Network from Multivariate Time Series with a Synthetic Method of Partial Symbolic Transfer Entropy Spectrum and Granger Causality

Topological Causality in Dynamical Systems

Long-Term Pulses of Dynamic Coupling Between Solar Hemispheres

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