scholarly journals Construction of complex networks from time series based on the cross correlation interval

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 253-260 ◽  
Author(s):  
Chen Feng ◽  
Bo He
Keyword(s):  
Time Series ◽  
Complex Networks ◽  
Complex Network ◽  
Cross Correlation ◽  
Clustering Coefficient ◽  
Two Phase ◽  
Correlation Interval ◽  
The Cross ◽  
The Lorenz System ◽  
Dynamic States

AbstractIn this paper, a new approach to map time series into complex networks based on the cross correlation interval is proposed for the analysis of dynamic states of time series on different scales. In the proposed approach, a time series is divided into time series segments and each segment is reconstructed to a phase space defined as a node of the complex network. The cross correlation interval, which characterizes the degree of correlation between two phase spaces, is computed as the distance between the two nodes. The clustering coefficient and efficiency are used to determine an appropriate threshold for the construction of a complex network that can effectively describe the dynamic states of a complex system. In order to verify the efficiency of the proposed approach, complex networks are constructed for time series generated from the Lorenz system, for white Gaussian noise time series and for sea clutter time series. The experimental results have demonstrated that nodes in different communities represent different dynamic states . Therefore, the proposed approach can be used to uncover the dynamic characteristics of the complex systems.

scholarly journals Complex Network Construction of Univariate Chaotic Time Series Based on Maximum Mean Discrepancy

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 142
Author(s):  
Jiancheng Sun
Keyword(s):  
Time Series ◽  
Complex Network ◽  
Gaussian Mixture ◽  
Chaotic Time Series ◽  
Network Construction ◽  
Maximum Mean Discrepancy ◽  
Univariate Time Series ◽  
Dimensional Phase Space ◽  
The Common ◽  
The Lorenz System

The analysis of chaotic time series is usually a challenging task due to its complexity. In this communication, a method of complex network construction is proposed for univariate chaotic time series, which provides a novel way to analyze time series. In the process of complex network construction, how to measure the similarity between the time series is a key problem to be solved. Due to the complexity of chaotic systems, the common metrics is hard to measure the similarity. Consequently, the proposed method first transforms univariate time series into high-dimensional phase space to increase its information, then uses Gaussian mixture model (GMM) to represent time series, and finally introduces maximum mean discrepancy (MMD) to measure the similarity between GMMs. The Lorenz system is used to validate the correctness and effectiveness of the proposed method for measuring the similarity.

scholarly journals Modeling Complex System Correlation Using Detrended Cross-Correlation Coefficient

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Keqiang Dong ◽  
Hong Zhang ◽  
You Gao
Keyword(s):  
Complex System ◽  
Time Series ◽  
Correlation Coefficient ◽  
Cross Correlation ◽  
Heavy Tails ◽  
Correlation Property ◽  
Traffic Time Series ◽  
Cross Correlations ◽  
The Cross ◽  
Active Research

The understanding of complex systems has become an area of active research for physicists because such systems exhibit interesting dynamical properties such as scale invariance, volatility correlation, heavy tails, and fractality. We here focus on traffic dynamic as an example of a complex system. By applying the detrended cross-correlation coefficient method to traffic time series, we find that the traffic fluctuation time series may exhibit cross-correlation characteristic. Further, we show that two traffic speed time series derived from adjacent sections exhibit much stronger cross-correlations than the two speed series derived from adjacent lanes. Similarly, we also demonstrate that the cross-correlation property between the traffic volume variables from two adjacent sections is stronger than the cross-correlation property between the volume variables of adjacent lanes.

scholarly journals Investigations of Broad Line Region Structure and Kinematics Using Variability

1989 ◽  
Vol 134 ◽  
pp. 93-95
Author(s):  
C. Martin Gaskell ◽  
Anuradha P. Koratkar ◽  
Linda S. Sparke
Keyword(s):  
Time Series ◽  
Cross Correlation ◽  
Sampling Interval ◽  
Broad Line ◽  
Line Flux ◽  
Line Region ◽  
Cross Correlations ◽  
The Mean ◽  
The Cross ◽  
The Continuum

Gaskell and Sparke (1986) showed that one can determine the sizes of BLRs more accurately that the mean sampling interval by cross-correlating the continuum flux time series with a line flux time series. The position of the peak in the cross-correlation function (CCF) and its shape give an indication of the BLR size. The technique is explained in detail in Gaskell and Peterson (1987). The widely propagated misunderstanding is that the method involves simply interpolating both time series and cross-correlating them (in which case the CCF is dominated by the cross-correlations of “made-up” data). Actually the method involves cross correlating the observed points in one time series (continuum, say) with the linear interpolations of the other series (line flux). The line flux time series must always be smoother than the continuum time series it is derived from. We have usually employed the method with the interpolation done both ways round and averaged them (to reduce errors due to the interpolation) and we can intercompare the two results (to investigate errors).

Multiscale Multifractal Detrended Cross-Correlation Analysis of High-Frequency Financial Time Series

2019 ◽  
Vol 18 (03) ◽  
pp. 1950014 ◽  
Author(s):  
Jingjing Huang ◽  
Danlei Gu
Keyword(s):  
Time Series ◽  
Correlation Analysis ◽  
High Frequency ◽  
Cross Correlation ◽  
Financial Time Series ◽  
Chinese Market ◽  
Change Of Scale ◽  
Cross Correlation Analysis ◽  
Cross Correlations ◽  
The Cross

In order to obtain richer information on the cross-correlation properties between two time series, we introduce a method called multiscale multifractal detrended cross-correlation analysis (MM-DCCA). This method is based on the Hurst surface and can be used to study the non-linear relationship between two time series. By sweeping through all the scale ranges of the multifractal structure of the complex system, it can present more information than the multifractal detrended cross-correlation analysis (MF-DCCA). In this paper, we use the MM-DCCA method to study the cross-correlations between two sets of artificial data and two sets of 5[Formula: see text]min high-frequency stock data from home and abroad. They are SZSE and SSEC in the Chinese market, and DJI and NASDAQ in the US market. We use Hurst surface and Hurst exponential distribution histogram to analyze the research objects and find that SSEC, SZSE and DJI, NASDAQ all show multifractal properties and long-range cross-correlations. We find that the fluctuation of the Hurst surface is related to the positive and negative of [Formula: see text], the change of scale range, the difference of national system, and the length of time series. The results show that the MM-DCCA method can give more abundant information and more detailed dynamic processes.

scholarly journals Complex networks from multivariate time series for characterizing nonlinear dynamics of two-phase flow patterns

2012 ◽  
Vol 61 (12) ◽  
pp. 120510
Author(s):  
Gao Zhong-Ke ◽  
Jin Ning-De ◽  
Yang Dan ◽  
Zhai Lu-Sheng ◽  
Du Meng
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
Complex Networks ◽  
Two Phase Flow ◽  
Multivariate Time Series ◽  
Flow Patterns ◽  
Phase Flow ◽  
Two Phase

Finding Hidden Communities in Complex Networks from Chaotic Time Series

2016 ◽  
Vol 3 (2) ◽  
pp. 350
Author(s):  
Jiancheng Sun
Keyword(s):  
Time Series ◽  
Complex Networks ◽  
Complex Network ◽  
Chaotic Time Series ◽  
Topology Structure ◽  
Complex Network Theory ◽  
Single Vertex ◽  
Reconstructed Phase Space ◽  
Information Coefficient ◽  
Maximal Information Coefficient

Recent works show that complex network theory may be another powerful tool in time series analysis. In this paper, we construct complex networks from the chaotic time series with Maximal Information Coefficient (MIC). Each vector point in the reconstructed phase space is represented by a single vertex and edge determined by MIC. By using the Chua’s circuit system, we illustrate the potential of these complex network measures for the detection of the topology structure of the network. Comparing with the linear relationship measure, we find that the topology structure of the community with MIC reveals the hidden or implied correlation of the network.

Building Complex Network Similar to Facebook

2014 ◽  
Vol 513-517 ◽  
pp. 909-913
Author(s):  
Dong Wei Guo ◽  
Xiang Yan Meng ◽  
Cai Fang Hou
Keyword(s):  
Social Networks ◽  
Social Network ◽  
Complex Networks ◽  
Complex Network ◽  
Network Model ◽  
Clustering Coefficient ◽  
Network Characteristics ◽  
Modeling Methods ◽  
Community Strength ◽  
Strength Based

Social networks have been developed rapidly, especially for Facebook which is very popular with 10 billion users. It is a considerable significant job to build complex network similar to Facebook. There are many modeling methods of complex networks but which cant describe characteristics similar to Facebook. This paper provide a building method of complex networks with tunable clustering coefficient and community strength based on BA network model to imitate Facebook. The strategies of edge adding based on link-via-triangular, link-via-BA and link-via-type are used to build a complex network with tunable clustering coefficient and community strength. Under different parameters, statistical properties of the complex network model are analyzed. The differences and similarities are studied among complex network model proposed by this paper and real social network on Facebook. It is found that the network characteristics of the network model and real social network on Facebook are similar under some specific parameters. It is proved that the building method of complex networks is feasible.

Temporal Dynamics of Streamflow Using Complex Networks

2020 ◽  
Author(s):  
Bellie Sivakumar
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Complex Networks ◽  
Chaos Theory ◽  
Temporal Dynamics ◽  
The United States ◽  
Phase Space Reconstruction ◽  
Clustering Coefficient ◽  
Network Construction ◽  
Original Time

<p>Modeling the dynamics of streamflow continues to be highly challenging. The present study proposes a new approach to study the temporal dynamics of streamflow. The approach couples the concepts of complex networks and chaos theory. Applications of the concepts of complex networks for studying streamflow dynamics have been gaining momentum in recent years. A key step in such applications is the construction of the network – a network is a set of points (nodes) connected by lines (links). The present study uses the concept of phase-space reconstruction, an essential first step in chaos theory-based methods, for network construction to study the temporal dynamics of streamflow. The phase-space reconstruction involves representation of a single-variable time series in a multi-dimensional phase space using delay embedding. The reconstructed phase space is treated as a network, with the reconstructed vectors (rather than the original time series) serving as the nodes and the connections between them serving as the links. With this network construction, the clustering coefficient of the individual nodes and the entire network is calculated to assess the node and network strengths. The approach is employed to a large number of streamflow time series observed in the United States. The results indicate the usefulness and effectiveness of the phase-space reconstruction-based approach for network construction. The implications of the outcomes for identification of the appropriate type and complexity of model as well as for classification of catchments are discussed.</p>

Generation of synthetic cross-correlated water demand time series

2013 ◽  
Vol 13 (4) ◽  
pp. 977-986 ◽  
Author(s):  
N. Ansaloni ◽  
S. Alvisi ◽  
M. Franchini
Keyword(s):  
Time Series ◽  
Water Demand ◽  
Distribution System ◽  
Water Distribution ◽  
Cross Correlation ◽  
Time Lags ◽  
Cross Correlations ◽  
The Cross ◽  
Water Districts

This paper presents a procedure for generating synthetic district-level series of hourly water demand coefficients cross-correlated in space (between districts) and time. The procedure consists of two steps: (1) generation of hourly water demand coefficients which respect, for each hour of the day, pre-assigned means and variances; and (2) introduction of the cross-correlation at different time lags through the application of a method which implies the reordering of the data generated at step 1. The procedure was applied to a case study of the Ferrara water distribution system with the aim of generating cross-correlated synthetic series of hourly water demand coefficients for the 19 water districts making it up. It was observed that the application of the method for introducing the cross-correlation (step 2) causes numerical problems when a large number of water districts are involved and the cross-correlations are considered at many time lags; this problem is solved by carrying out an appropriate regularization of the observed cross-correlation matrix. The results obtained show that overall the proposed procedure constitutes a valid tool for generating synthetic water demand time series with pre-assigned characteristics in terms of means, variances and cross-correlation at different time lags.

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