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On the Similarity and Dependence of Time Series

Author

Listed:
  • Vilém Novák

    (Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, NSC IT4Innovations, 30. dubna 22, 701 03 Ostrava 1, Czech Republic)

  • Soheyla Mirshahi

    (Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, NSC IT4Innovations, 30. dubna 22, 701 03 Ostrava 1, Czech Republic)

Abstract

In this paper, we undertake the problem of evaluating interrelation among time series. Interrelation is measured using a similarity index. In this paper, we suggest a new one based on the known fuzzy transform (F-transform), which has been proven to remove higher frequencies than a given threshold and reduce the random noise significantly. The F-transform also provides an estimation of the slope of time series in a given imprecisely delineated time. We prove some of the suggested index properties and show its ability to measure similarity (and thus the interrelation) on a selection of several real financial time series. The method is well interpretable and easy to adjust.

Suggested Citation

  • Vilém Novák & Soheyla Mirshahi, 2021. "On the Similarity and Dependence of Time Series," Mathematics, MDPI, vol. 9(5), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:550-:d:511361
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    References listed on IDEAS

    as
    1. Mills,Terence C. & Markellos,Raphael N., 2008. "The Econometric Modelling of Financial Time Series," Cambridge Books, Cambridge University Press, number 9780521710091, September.
    2. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871, September.
    3. R. Mantegna, 1999. "Hierarchical structure in financial markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 11(1), pages 193-197, September.
    4. Qiang Yang & Xindong Wu, 2006. "10 Challenging Problems In Data Mining Research," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 5(04), pages 597-604.
    5. Mills,Terence C. & Markellos,Raphael N., 2008. "The Econometric Modelling of Financial Time Series," Cambridge Books, Cambridge University Press, number 9780521883818.
    6. Leonidas Sandoval Junior & Asher Mullokandov & Dror Y. Kenett, 2015. "Dependency Relations among International Stock Market Indices," JRFM, MDPI, vol. 8(2), pages 1-39, May.
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    Cited by:

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