IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v445y2016icp1-17.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437115008961
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2015.10.041?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wu, Han-Ming & Tien, Yin-Jing & Chen, Chun-houh, 2010. "GAP: A graphical environment for matrix visualization and cluster analysis," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 767-778, March.
    2. José E. Chacón, 2021. "Explicit Agreement Extremes for a 2 × 2 Table with Given Marginals," Journal of Classification, Springer;The Classification Society, vol. 38(2), pages 257-263, July.
    3. Xu, Mengjia & Shang, Pengjian & Lin, Aijing, 2017. "Multiscale recurrence quantification analysis of order recurrence plots," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 381-389.
    4. Roberto Rocci & Stefano Antonio Gattone & Roberto Di Mari, 2018. "A data driven equivariant approach to constrained Gaussian mixture modeling," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(2), pages 235-260, June.
    5. Redivo, Edoardo & Nguyen, Hien D. & Gupta, Mayetri, 2020. "Bayesian clustering of skewed and multimodal data using geometric skewed normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    6. Zhu, Xuwen & Melnykov, Volodymyr, 2018. "Manly transformation in finite mixture modeling," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 190-208.
    7. Amiri, Babak & Karimianghadim, Ramin, 2024. "A novel text clustering model based on topic modelling and social network analysis," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    8. Li, Pai-Ling & Chiou, Jeng-Min, 2011. "Identifying cluster number for subspace projected functional data clustering," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2090-2103, June.
    9. A van Giessen & K G M Moons & G A de Wit & W M M Verschuren & J M A Boer & H Koffijberg, 2015. "Tailoring the Implementation of New Biomarkers Based on Their Added Predictive Value in Subgroups of Individuals," PLOS ONE, Public Library of Science, vol. 10(1), pages 1-14, January.
    10. Yaeji Lim & Hee-Seok Oh & Ying Kuen Cheung, 2019. "Multiscale Clustering for Functional Data," Journal of Classification, Springer;The Classification Society, vol. 36(2), pages 368-391, July.
    11. Stefano Tonellato & Andrea Pastore, 2013. "On the comparison of model-based clustering solutions," Working Papers 2013:05, Department of Economics, University of Venice "Ca' Foscari".
    12. Elvira Pelle & Roberta Pappadà, 2021. "A clustering procedure for mixed-type data to explore ego network typologies: an application to elderly people living alone in Italy," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(5), pages 1507-1533, December.
    13. Renato Cordeiro Amorim, 2016. "A Survey on Feature Weighting Based K-Means Algorithms," Journal of Classification, Springer;The Classification Society, vol. 33(2), pages 210-242, July.
    14. Tom Wilderjans & Eva Ceulemans & Iven Mechelen, 2008. "The CHIC Model: A Global Model for Coupled Binary Data," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 729-751, December.
    15. Dong Liu & Changwei Zhao & Yong He & Lei Liu & Ying Guo & Xinsheng Zhang, 2023. "Simultaneous cluster structure learning and estimation of heterogeneous graphs for matrix‐variate fMRI data," Biometrics, The International Biometric Society, vol. 79(3), pages 2246-2259, September.
    16. Yuchen Liang & Guowei Shi & Runlin Cai & Yuchen Yuan & Ziying Xie & Long Yu & Yingjian Huang & Qian Shi & Lizhe Wang & Jun Li & Zhonghui Tang, 2024. "PROST: quantitative identification of spatially variable genes and domain detection in spatial transcriptomics," Nature Communications, Nature, vol. 15(1), pages 1-17, December.
    17. Jeffrey Andrews & Paul McNicholas, 2014. "Variable Selection for Clustering and Classification," Journal of Classification, Springer;The Classification Society, vol. 31(2), pages 136-153, July.
    18. Marek Obrębalski & Marek Walesiak, 2015. "Functional structure of Polish regions in the period 2004-2013 – measurement via HHI Index, Florence’s coefficient of localization and cluster analysis," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 16(2), pages 223-242, June.
    19. Luca Scaffidi Domianello & Giampiero M. Gallo & Edoardo Otranto, 2024. "Smooth and Abrupt Dynamics in Financial Volatility: The MS‐MEM‐MIDAS," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 86(1), pages 21-43, February.
    20. Paul Bastide & Mahendra Mariadassou & Stéphane Robin, 2017. "Detection of adaptive shifts on phylogenies by using shifted stochastic processes on a tree," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 1067-1093, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:445:y:2016:i:c:p:1-17. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.