From time series to complex networks: The phase space coarse graining

In this paper, we present a simple and fast computational method, the phase space coarse graining algorithm that converts a time series into a directed and weighted complex network. The constructed directed and weighted complex network inherits several properties of the series in its structure. Thereby, periodic series convert into regular networks, and random series do so into random networks. Moreover, chaotic series convert into scale-free networks. It is shown that the phase space coarse graining algorithm allows us to distinguish, identify and describe in detail various time series. Finally, we apply the phase space coarse graining algorithm to the practical observations series, international gasoline regular spot price series and identify its dynamic characteristics.

[1]  Epaminondas Panas,et al.  Are oil markets chaotic? A non-linear dynamic analysis , 2000 .

[2]  M Small,et al.  Detecting chaos in pseudoperiodic time series without embedding. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Jie Liu,et al.  COMPARISON OF DIFFERENT DAILY STREAMFLOW SERIES IN US AND CHINA, UNDER A VIEWPOINT OF COMPLEX NETWORKS , 2010 .

[4]  Lixin Tian,et al.  Regulating effect of the energy market—Theoretical and empirical analysis based on a novel energy prices–energy supply–economic growth dynamic system , 2015 .

[5]  P. Erdos,et al.  On the existence of a factor of degree one of a connected random graph , 1966 .

[6]  Wei-Xing Zhou,et al.  Statistical properties of visibility graph of energy dissipation rates in three-dimensional fully developed turbulence , 2009, 0905.1831.

[7]  Yun Long.  Visibility graph network analysis of gold price time series , 2013 .

[8]  Zhou Ting-Ting,et al.  Limited penetrable visibility graph for establishing complex network from time series , 2012 .

[9]  Jinjun Tang,et al.  Characterizing traffic time series based on complex network theory , 2013 .

[10]  Norbert Marwan,et al.  The geometry of chaotic dynamics — a complex network perspective , 2011, 1102.1853.

[11]  P. Grassberger,et al.  Characterization of Strange Attractors , 1983 .

[12]  M. Newman,et al.  Renormalization Group Analysis of the Small-World Network Model , 1999, cond-mat/9903357.

[13]  M. Small,et al.  Characterizing pseudoperiodic time series through the complex network approach , 2008 .

[14]  Zhi-Qiang Jiang,et al.  Degree distributions of the visibility graphs mapped from fractional Brownian motions and multifractal random walks , 2008, 0812.2099.

[15]  Michael Small,et al.  Recurrence-based time series analysis by means of complex network methods , 2010, Int. J. Bifurc. Chaos.

[16]  Michael Small,et al.  Detecting temporal and spatial correlations in pseudoperiodic time series. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[18]  Z. Shao.  Network analysis of human heartbeat dynamics , 2010 .

[19]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[20]  Norbert Marwan,et al.  Identification of dynamical transitions in marine palaeoclimate records by recurrence network analysis , 2011 .

[21]  M Small,et al.  Complex network from pseudoperiodic time series: topology versus dynamics. , 2006, Physical review letters.

[22]  Zhao Dong,et al.  Comment on “Network analysis of human heartbeat dynamics” [Appl. Phys. Lett. 96, 073703 (2010)] , 2010 .

[23]  Michael Small,et al.  Multiscale characterization of recurrence-based phase space networks constructed from time series. , 2012, Chaos.

[24]  Yue Yang,et al.  Visibility graph approach to exchange rate series , 2009 .

[25]  Lucas Lacasa,et al.  From time series to complex networks: The visibility graph , 2008, Proceedings of the National Academy of Sciences.

[26]  Zonghua Liu,et al.  Network analysis of time series under the constraint of fixed nearest neighbors , 2013 .

[27]  Michael Small,et al.  Superfamily phenomena and motifs of networks induced from time series , 2008, Proceedings of the National Academy of Sciences.

[28]  M. Small,et al.  Characterizing system dynamics with a weighted and directed network constructed from time series data. , 2014, Chaos.

[29]  Huajiao Li,et al.  Features and evolution of international crude oil trade relationships: A trading-based network analysis , 2014 .

[30]  Haizhong An,et al.  The role of fluctuating modes of autocorrelation in crude oil prices , 2014 .

[31]  Emily A. Fogarty,et al.  Visibility network of United States hurricanes , 2009 .

[32]  Zhi-Qiang Jiang,et al.  Universal and nonuniversal allometric scaling behaviors in the visibility graphs of world stock market indices , 2009, 0910.2524.

[33]  J. C. Nuño,et al.  The visibility graph: A new method for estimating the Hurst exponent of fractional Brownian motion , 2009, 0901.0888.

[34]  Jurgen Kurths,et al.  Testing time series irreversibility using complex network methods , 2012, 1211.1162.

[35]  Dachuan Wei,et al.  An Optimized Floyd Algorithm for the Shortest Path Problem , 2010, J. Networks.

[36]  Zhongke Gao,et al.  Complex network from time series based on phase space reconstruction. , 2009, Chaos.

[37]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[38]  B. Luque,et al.  Horizontal visibility graphs: exact results for random time series. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  Hojjat Adeli,et al.  New diagnostic EEG markers of the Alzheimer’s disease using visibility graph , 2010, Journal of Neural Transmission.

[40]  J. Salas,et al.  Nonlinear dynamics, delay times, and embedding windows , 1999 .