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Coupling between time series: a network view

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

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    File URL: http://arxiv.org/pdf/1301.1010
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1301.1010.

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    Date of creation: Jan 2013
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    Handle: RePEc:arx:papers:1301.1010

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    Web page: http://arxiv.org/

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