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Coupling between time series: a network view

Author

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

Abstract

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.

Suggested Citation

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

    1. Liu, Jin-Long & Yu, Zu-Guo & Zhou, Yu, 2024. "A cross horizontal visibility graph algorithm to explore associations between two time series," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    2. Jamshid Ardalankia & Jafar Askari & Somaye Sheykhali & Emmanuel Haven & G. Reza Jafari, 2020. "Mapping Coupled Time-series Onto Complex Network," Papers 2004.13536, arXiv.org, revised Aug 2020.

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