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Coupling between time series: a network view


  • Saeed Mehraban
  • Amirhossein Shirazi
  • Maryam Zamani
  • Gholamreza Jafari


Recently, the visibility graph has been introduced as a novel view for analyzing time series, which maps it to a complex network. In this paper, we introduce new algorithm of visibility, "cross-visibility", which reveals the conjugation of two coupled time series. The correspondence between the two time series is mapped to a network, "the cross-visibility graph", to demonstrate the correlation between them. We applied the algorithm to several correlated and uncorrelated time series, generated by the linear stationary ARFIMA process. The results demonstrate that the cross-visibility graph associated with correlated time series with power-law auto-correlation is scale-free. If the time series are uncorrelated, the degree distribution of their cross-visibility network deviates from power-law. For more clarifying the process, we applied the algorithm to real-world data from the financial trades of two companies, and observed significant small-scale coupling in their dynamics.

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  • Saeed Mehraban & Amirhossein Shirazi & Maryam Zamani & Gholamreza Jafari, 2013. "Coupling between time series: a network view," Papers 1301.1010,
  • Handle: RePEc:arx:papers:1301.1010

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    1. Cox, John C. & Leland, Hayne E., 2000. "On dynamic investment strategies," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1859-1880, October.
    2. Carole Bernard & Phelim P. Boyle & Steven Vanduffel, 2014. "Explicit Representation of Cost-Efficient Strategies," Finance, Presses universitaires de Grenoble, vol. 35(2), pages 5-55.
    3. He Hua & Huang Chi-fu, 1994. "Consumption-Portfolio Policies: An Inverse Optimal Problem," Journal of Economic Theory, Elsevier, vol. 62(2), pages 257-293, April.
    4. Daniel G. Goldstein & Eric J. Johnson & William F. Sharpe, 2008. "Choosing Outcomes versus Choosing Products: Consumer-Focused Retirement Investment Advice," Journal of Consumer Research, Oxford University Press, vol. 35(3), pages 440-456, August.
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