Recurrence-based time series analysis by means of complex network methods

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 with 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.Comment: To be published in International Journal of Bifurcation and Chaos (2011

Synchronization in complex networks

Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization phenomena in natural systems take now advantage of the recent theory of complex networks. In this review, we report the advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology. We also overview the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections. Extensive numerical work as well as analytical approaches to the problem are presented. Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences.Comment: Final version published in Physics Reports. More information available at http://synchronets.googlepages.com

Complex network analysis and nonlinear dynamics

This chapter aims at reviewing complex network and nonlinear dynamical models and methods that were either developed for or applied to socioeconomic issues, and pertinent to the theme of New Economic Geography. After an introduction to the foundations of the field of complex networks, the present summary introduces some applications of complex networks to economics, finance, epidemic spreading of innovations, and regional trade and developments. The chapter also reviews results involving applications of complex networks to other relevant socioeconomic issue

Recurrence networks - A novel paradigm for nonlinear time series analysis

This paper presents a new approach for analysing structural properties of time series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency matrix of an associated complex network which links different points in time if the evolution of the considered states is very similar. A critical comparison of these recurrence networks with similar existing techniques is presented, revealing strong conceptual benefits of the new approach which can be considered as a unifying framework for transforming time series into complex networks that also includes other methods as special cases. It is demonstrated that there are fundamental relationships between the topological properties of recurrence networks and the statistical properties of the phase space density of the underlying dynamical system. Hence, the network description yields new quantitative characteristics of the dynamical complexity of a time series, which substantially complement existing measures of recurrence quantification analysis

Predicting the state of synchronization of financial time series using cross recurrence plots

Cross-correlation analysis is a powerful tool for understanding the mutual dynamics of time series. This study introduces a new method for predicting the future state of synchronization of the dynamics of two financial time series. To this end, we use the cross recurrence plot analysis as a nonlinear method for quantifying the multidimensional coupling in the time domain of two time series and for determining their state of synchronization. We adopt a deep learning framework for methodologically addressing the prediction of the synchronization state based on features extracted from dynamically sub-sampled cross recurrence plots. We provide extensive experiments on several stocks, major constituents of the S &P100 index, to empirically validate our approach. We find that the task of predicting the state of synchronization of two time series is in general rather difficult, but for certain pairs of stocks attainable with very satisfactory performance (84% F1-score, on average)

Reconstructing dynamical networks via feature ranking

Empirical data on real complex systems are becoming increasingly available. Parallel to this is the need for new methods of reconstructing (inferring) the topology of networks from time-resolved observations of their node-dynamics. The methods based on physical insights often rely on strong assumptions about the properties and dynamics of the scrutinized network. Here, we use the insights from machine learning to design a new method of network reconstruction that essentially makes no such assumptions. Specifically, we interpret the available trajectories (data) as features, and use two independent feature ranking approaches -- Random forest and RReliefF -- to rank the importance of each node for predicting the value of each other node, which yields the reconstructed adjacency matrix. We show that our method is fairly robust to coupling strength, system size, trajectory length and noise. We also find that the reconstruction quality strongly depends on the dynamical regime

Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package

We introduce the \texttt{pyunicorn} (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. \texttt{pyunicorn} is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics or network surrogates. Additionally, \texttt{pyunicorn} provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis (RQA), recurrence networks, visibility graphs and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.Comment: 28 pages, 17 figure

Concordance in global office market cycles

A large proportion of international real estate investment is concentrated in the office markets of the world’s largest cities. However, many of these global cities are also key financial services centres, highlighting the possibility of reduced economic diversification from an investor’s perspective. This paper assesses the degree of synchronization in cycles across twenty of the world’s largest office markets, finding evidence of significant concordance across a large number of markets. The results highlight the problems associated with commonalities in the underlying economic bases of the markets. The concentration of investment also raises the possibility of common flow of funds effects that may further reduce diversification opportunities

Collective behavior in financial market

Financial market is an example of complex system, which is characterized by a highly intricate organization and the emergence of collective behavior. In this paper, we quantify this emergent dynamics in the financial market by using concepts of network synchronization. We consider networks constructed by the correlation matrix of asset returns and study the time evolution of the phase coherence among stock prices. It is verified that during financial crisis a synchronous state emerges in the system, defining the market's direction. Furthermore, the paper proposes a statistical regression model able to identify the topological features that mostly influence such an emergence. The coefficients of the proposed model indicate that the average shortest path length is the measurement most related to network synchronization. Therefore, during economic crisis, the stock prices present a similar evolution, which tends to shorten the distances between stocks, indication a collective dynamics.Comment: 5 pages, 2 figure