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Finding metastable states in real-world time series with recurrence networks

Author

Listed:
  • Vega, I.
  • Schütte, Ch.
  • Conrad, T.O.F.

Abstract

In the framework of time series analysis with recurrence networks, we introduce a self-adaptive method that determines the elusive recurrence threshold and identifies metastable states in complex real-world time series. As initial step, we introduce a way to set the embedding parameters used to reconstruct the state space from the time series. We set them as the ones giving the maximum Shannon entropy of the diagonal line length distribution for the first simultaneous minima of recurrence rate and Shannon entropy. To identify metastable states, as well as the transitions between them, we use a soft partitioning algorithm for module finding which is specifically developed for the case in which a system shows metastability. We illustrate our method with a complex time series example. Finally, we show the robustness of our method for identifying metastable states. Our results suggest that our method is robust for identifying metastable states in complex time series, even when introducing considerable levels of noise and missing data points.

Suggested Citation

  • Vega, I. & Schütte, Ch. & Conrad, T.O.F., 2016. "Finding metastable states in real-world time series with recurrence networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 1-17.
    • Handle: RePEc:eee:phsmap:v:445:y:2016:i:c:p:1-17
    DOI: 10.1016/j.physa.2015.10.041
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    References listed on IDEAS

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    1. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    2. R. Donner & J. Heitzig & J. Donges & Y. Zou & N. Marwan & J. Kurths, 2011. "The geometry of chaotic dynamics — a complex network perspective," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 84(4), pages 653-672, December.
    3. Chen, Yun & Yang, Hui, 2012. "Multiscale recurrence analysis of long-term nonlinear and nonstationary time series," Chaos, Solitons & Fractals, Elsevier, vol. 45(7), pages 978-987.
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    Cited by:

    1. Chen, Yuan & Lin, Aijing, 2022. "Order pattern recurrence for the analysis of complex systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    2. Rounaghi, Mohammad Mahdi & Nassir Zadeh, Farzaneh, 2016. "Investigation of market efficiency and Financial Stability between S&P 500 and London Stock Exchange: Monthly and yearly Forecasting of Time Series Stock Returns using ARMA model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 10-21.

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