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Time Series: How Unusual Local Behavior Can Be Recognized Using Fuzzy Modeling Methods

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Statistical and Fuzzy Approaches to Data Processing, with Applications to Econometrics and Other Areas

Part of the book series: Studies in Computational Intelligence ((SCI,volume 892))

Abstract

In this paper, we address the problem of automatic recognition of structural breaks in time series. The former are unexpected shifts of the course or sudden change of the volatility of time series. Structural breaks can be caused, e.g., by changes in the organization of a company, global or local economic development, global shifts in capital and labor, various kinds of outer influences such as discovery or depletion of natural resources, etc. Structural breaks in time series are usually detected using statistical methods. In this paper, we suggest using special non-statistical techniques of fuzzy modeling. We will employ two classes of them, namely the fuzzy transform (F-transform) and selected methods of Fuzzy Natural Logic (FNL). The fuzzy transform enables us to estimate the average slope of time series in an area characterized by a fuzzy set. The slope is then evaluated by evaluative linguistic expressions, which enables us to identify intervals with monotonous behavior and, consequently, identify structural breaks. Our method is simple, transparent, and computationally effective.

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Notes

  1. 1.

    We will use the term “inverse fuzzy transform” in two meanings: (a) as the procedure for obtaining estimation of f and (b), as the function (10) approximating f.

  2. 2.

    Without lack of generality, we may assume that \(U\subset \mathbb {R}\).

  3. 3.

    Such a function is called intension.

  4. 4.

    Or, precisely, \(v_S=v_L+(v_R-v_L)*(1-\frac{1}{\varphi })\).

  5. 5.

    Let us remind the Zadeh’s concept of precisiated natural language [25] that is considered as a technical simplification that works well in most practical situations.

  6. 6.

    We consider here again the golden ratio.

  7. 7.

    https://forecasters.org/resources/time-series-data/m3-competition/.

  8. 8.

    The software was developed in the Institute for Research of Applications of Fuzzy Modeling of the University of Ostrava, Czech Republic.

  9. 9.

    Only full inner components are considered.

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Acknowledgments

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, University of Ostrava, NSC IT4Innovations, 30. dubna 22, 70103, Ostrava 1, Czech Republic

    Vilém Novák & Viktor Pavliska

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  1. Vilém Novák
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  2. Viktor Pavliska
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Correspondence to Vilém Novák .

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Editors and Affiliations

  1. Department of Computer Science, University of Texas at El Paso, El Paso, TX, USA

    Vladik Kreinovich

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Novák, V., Pavliska, V. (2021). Time Series: How Unusual Local Behavior Can Be Recognized Using Fuzzy Modeling Methods. In: Kreinovich, V. (eds) Statistical and Fuzzy Approaches to Data Processing, with Applications to Econometrics and Other Areas. Studies in Computational Intelligence, vol 892. Springer, Cham. https://doi.org/10.1007/978-3-030-45619-1_13

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