Mapping stochastic processes onto complex networks

Shirazi, Amir Hossein Masnadi; Jafari, G. R.; Davoudi, Jahanshah; Peinke, Joachim; Tabar, M. Reza Rahimi; Sahimi, Muhammad

doi:10.1088/1742-5468/2009/07/p07046

Cited by 79 publications

(67 citation statements)

References 29 publications

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“…. , S K } allows considering the transition probabilities π α,β = P (x i+1 ∈ S β | x i ∈ S α ) between these classes in terms of a weighted and directed network [Nicolis et al, 2005;Dellnitz et al, 2006;Gao & Li, 2005;Li & Gao, 2006;Gao et al, 2007;Li & Wang, 2006;Li & Wang, 2007;Shirazi et al, 2009;Padberg et al, 2009]. This approach is equivalent to applying a symbolic discretization with static grouping [Daw et al, 2003;Donner et al, 2008] to the phase space of the studied system.…”

Section: Transition Networkmentioning

confidence: 99%

Recurrence-Based Time Series Analysis by Means of Complex Network Methods

Donner

Small

Donges

et al. 2011

Int. J. Bifurcation Chaos

373

338

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Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts have been spent on applying network-based concepts also for the analysis of dynamically relevant higher-order statistical properties of time series. Notably, many corresponding approaches are closely related to the concept of recurrence in phase space. In this paper, we review recent methodological advances in time series analysis based on complex networks, with a special emphasis on methods founded on recurrence plots. The potentials and limitations of the individual methods are discussed and illustrated for paradigmatic examples of dynamical systems as well as for real-world time series. Complex network measures are shown to provide information about structural features of dynamical systems that are complementary to those characterized by other methods of time series analysis and, hence, substantially enrich the knowledge gathered from other existing (linear as well as nonlinear) approaches.

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Section: Transition Networkmentioning

confidence: 99%

Recurrence-Based Time Series Analysis by Means of Complex Network Methods

Donner

Small

Donges

et al. 2011

Int. J. Bifurcation Chaos

373

338

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“…The time series firstly is transformed into networks and then analyzed with various complex network tools [25][26][27][28]. Shirazi et al [29] demonstrated that the time series can be reconstructed with high precision by means of a simple random walk on their corresponding networks. The interaction of financial markets naturally constitutes a complex system in which the stock data are a multivariate time series (MTS) [30] of information in each part of the complex system.…”

Section: Introductionmentioning

confidence: 99%

Construction of Complex Network with Multiple Time Series Relevance

Huang

Wang³

et al. 2018

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Multivariate time series data, which comprise a set of ordered observations for multiple variables, are pervasively generated in weather conditions, traffic, financial stocks, etc. Therefore, it is of great significance to analyze the correlation between multiple time series. Financial stocks generate a significant amount of multivariate time series data that can be used to build networks that reflect market behavior. However, traditional commercial complex networks cannot fully utilize the multiple attributes of stocks and redundant filter relationships and reveal a more authentic financial stock market. We propose a fusion similarity of multiple time series and construct a threshold network with similarity. Furthermore, we define the connectivity efficiency to choose the best threshold, establishing a high connectivity efficiency network with the optimal network threshold. By searching the central node in the threshold network, we have found that the network center nodes constructed by our proposed method have a more comprehensive industry coverage than the traditional techniques to build the systems, and this also proves the superiority of this method.

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“…More recently, a graphtheoretical approach in time series analysis has been developed, and the network-based theories have been applied in many disciplines such as biology, sociology, physics, climatology, and neurosciences [24][25][26][27][28][29][30][31] . In this approach, a time series is mapped into a (complex) graph, and the characteristics of the time series are believed to be inherited in the resulting network, which can be analyzed from a complex network perspective.…”

Section: Introductionmentioning

confidence: 99%

Complex network approach to fractional time series

Manshour

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In order to extract correlation information inherited in stochastic time series, the visibility graph algorithm has been recently proposed, by which a time series can be mapped onto a complex network. We demonstrate that the visibility algorithm is not an appropriate one to study the correlation aspects of a time series. We then employ the horizontal visibility algorithm, as a much simpler one, to map fractional processes onto complex networks. The degree distributions are shown to have parabolic exponential forms with Hurst dependent fitting parameter. Further, we take into account other topological properties such as maximum eigenvalue of the adjacency matrix and the degree assortativity, and show that such topological quantities can also be used to predict the Hurst exponent, with an exception for anti-persistent fractional Gaussian noises. To solve this problem, we take into account the Spearman correlation coefficient between nodes' degrees and their corresponding data values in the original time series.

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Mapping stochastic processes onto complex networks

Cited by 79 publications

References 29 publications

Recurrence-Based Time Series Analysis by Means of Complex Network Methods

Recurrence-Based Time Series Analysis by Means of Complex Network Methods

Construction of Complex Network with Multiple Time Series Relevance

Complex network approach to fractional time series

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