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Measuring persistence in a stationary time series using the complex network theory

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  • Karimi, Somaye
  • Darooneh, Amir H.

Abstract

A growing interest exists currently in the analysis of time series by the complex network theory. Here we present a simple and quick way for mapping time series to complex networks. Using a simple rule allows us to transform time series into a textual sequence then we divide it into words with fixed size. Distinct words are nodes of the network, and we have complete control on the network scale by adjusting the word size. Two nodes are linked if their associated words co-occur in sequence. We show that the network topological measures quantify the persistence and the long range correlations in fractional Brownian processes. For a particular word size we assume some relations between the topological measures and the Hurst exponent which characterised the persistence in fractional Brownian processes.

Suggested Citation

  • Karimi, Somaye & Darooneh, Amir H., 2013. "Measuring persistence in a stationary time series using the complex network theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(1), pages 287-293.
  • Handle: RePEc:eee:phsmap:v:392:y:2013:i:1:p:287-293
    DOI: 10.1016/j.physa.2012.07.077
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    Cited by:

    1. An, Haizhong & Gao, Xiangyun & Fang, Wei & Huang, Xuan & Ding, Yinghui, 2014. "The role of fluctuating modes of autocorrelation in crude oil prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 382-390.
    2. Tang, Jinjun & Wang, Yinhai & Wang, Hua & Zhang, Shen & Liu, Fang, 2014. "Dynamic analysis of traffic time series at different temporal scales: A complex networks approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 303-315.
    3. Zhou, Jin & Xu, Weixiang & Guo, Xin & Liu, Xumin, 2017. "A hierarchical network modeling method for railway tunnels safety assessment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 226-239.

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