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A fuzzy method for evaluating similar behavior between assets

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Abstract

In this paper, we propose a fuzzy method to investigate the interconnection between equity markets in the form of similar behavior. It has been proved before that the trend cycle of time series can be well estimated using the fuzzy transform. In the suggested method, first, we approximate the local behavior of stocks as a sequence of their trend cycles. Then we measure the distance between these local trend cycles conducting similar practices between different assets. Two experiments are performed to demonstrate the advantages of the suggested method. This method is easy to calculate, well interpretable, and in addition to statistical co-relation, the measure can assist investors in gaining more intuition about the behavior of their assets.

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Notes

  1. Of course, certain formal requirements must be fulfilled. They are omitted here and can be found in the cited literature.

  2. In general, higher degree F-transform.

  3. Modulus of continuity is in our case defined as \(\omega (h, { T\!C})=\max _{\begin{array}{c} |x-y|<h\\ x,y\in [c_1, c_{n-1}] \end{array}}|{ T\!C}(x)-{ T\!C}(y)|\).

  4. A t-norm is a special operation that in fuzzy logic models logical conjunction.

  5. It is necessary to emphasize, that we can work with estimations \({ \widetilde{T\!C}}_X\) and \({ \widetilde{T\!C}}_Y\) of the trend cycle only, because we do not know the real ones.

  6. https://www.nasdaq.com/Second footnote

  7. https://www.nasdaq.com/Second footnote.

  8. www.finance.yahoo.com.

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Acknowledgements

The paper has been supported by the grant 18-13951S of GAČR, Czech Republic.

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Authors and Affiliations

  1. Institute for Research and Applications of Fuzzy Modeling, NSC IT4Innovations, University of Ostrava, Ostrava, Czech Republic

    Soheyla Mirshahi & Vilém Novák

Authors
  1. Soheyla Mirshahi
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  2. Vilém Novák
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Soheyla Mirshahi and Vilém Novák. The first draft of the manuscript was written by both authors, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Soheyla Mirshahi.

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Communicated by Vladik Kreinovich.

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Mirshahi, S., Novák, V. A fuzzy method for evaluating similar behavior between assets. Soft Comput 25, 7813–7823 (2021). https://doi.org/10.1007/s00500-021-05639-y

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