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Nonstatistical Methods for Analysis, Forecasting, and Mining Time Series

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Theory and Applications of Time Series Analysis and Forecasting (ITISE 2021)

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Abstract

This is an overview paper, in which we briefly present results obtained over several years in the analysis, forecasting, and mining information from time series using methods that predominantly have nonstatistical character. Our main goal is to show the readers from the area of probability theory and statistics that nonstatistical methods can be pretty successful in time series processing. Besides the standard tasks such as estimation of trend/trend-cycle and forecasting, our methods are also powerful in providing additional information that can hardly be obtained using the statistical methods, namely, evaluation of the local course, finding perceptually important points, identification of structural breaks, finding periods of monotonous behavior including its evaluation, or summarization of information about large sets of time series. Our goal is not to beat statistical methods, but vice versa—to benefit from the synergy of both.

The work was supported from ERDF/ESF by the project “Centre for the development of Artificial Intelligence Methods for the Automotive Industry of the region” No. CZ.02.1.01/0.0/0.0/17-049/0008414.

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Notes

  1. 1.

    The interval [0,  1] is a set of truth values where 0 means falsity, 1 truth, and the other values express partial truth. This interval can be replaced by a suitable bounded lattice.

  2. 2.

    It has a good sense to speak about the probability of fuzzy events. For example, what is the probability that in the next few minutes, we will meet a tall woman.

  3. 3.

    Such a function is implemented in the experimental software LFL Forecaster (see http://irafm.osu.cz/en/c110_lfl-forecaster/) developed in the Inst. for Research and Applications of Fuzzy Modeling of the University of Ostrava, Czech Republic, which implements the described methods. Its author is Viktor Pavliska. The results demonstrated in this paper were obtained using the mentioned software.

References

  1. Anděl, J.: Statistical Analysis of Time Series. SNTL, Praha (1976 (in Czech))

    Google Scholar 

  2. Bovas, A., Ledolter, J.: Statistical Methods for Forecasting. Wiley, New York (2003)

    MATH  Google Scholar 

  3. Castillo-Ortega, R., Marín, N., Sánchez, D.: A fuzzy approach to the linguistic summarization of time series. Multiple Val. Logic Soft Comput. 17(2-3), 157–182 (2011)

    Google Scholar 

  4. De Wachter, S., Tzavalis, D.: Detection of structural breaks in linear dynamic panel data models. Computat. Stat. Data Anal. 56(11), 3020–3034 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  5. Doerr, B., Fischer, P., Hilbert, A., Witt, C.: Detecting structural breaks in time series via genetic algorithms. Soft Computing 21(16), 4707–4720 (2017)

    Article  Google Scholar 

  6. Dvořák, A., Holčapek, M.: L-fuzzy quantifiers of the type 〈1〉 determined by measures. Fuzzy Sets Syst. 160, 3425–3452 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Fu, T.C.: A review on time series data mining. Eng. Appl. Artif. Intell. 24, 164–181 (2011)

    Article  Google Scholar 

  8. Hamilton, J.: Time Series Analysis. Princeton, Princeton University Press (1994)

    Book  MATH  Google Scholar 

  9. Kacprzyk, J., Wilbik, A., Zadrożny, S.: Linguistic summarization of time series using a fuzzy quantifier driven aggregation. Fuzzy Sets Syst. 159, 1485–1499 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  10. Kacprzyk, J., Wilbik, A., Zadrożny, S.: An approach to the linguistic summarization of time series using a fuzzy quantifier driven aggregation. Int. J. Intell. Syst. 25, 411–439 (2010)

    MATH  Google Scholar 

  11. Kreinovich, V., Perfilieva, I.: Fuzzy transforms of higher order approximate derivatives: A theorem. Fuzzy Sets Syst. 180, 55–68 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. Mirshahi, S., Novák, V.: A fuzzy method for evaluating similar behaviour between assets. Soft Computing 25, 7813–7823 (2021)

    Article  Google Scholar 

  13. Moyse, G., Lesot, M.: Linguistic summaries of locally periodic time series. Fuzzy Sets Syst. 285, 94–117 (2016)

    Article  MathSciNet  Google Scholar 

  14. Murinová, P., Novák, V.: A formal theory of generalized intermediate syllogisms. Fuzzy Sets Syst. 186, 47–80 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  15. Murinová, P., Novák, V.: The structure of generalized intermediate syllogisms. Fuzzy Sets Syst. 247, 18–37 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  16. Nguyen, L., Holčapek, M.: Suppression of high frequencies in time series using fuzzy transform of higher degree. In: Carvalho, J., et al. (eds.) Information Processing and Management of Uncertainty in Knowledge-Based Systems: 16th International Conference, IPMU 2016, vol. 2, pp. 705–716. Springer (2016)

    Google Scholar 

  17. Nguyen, L., Holčapek, M.: Higher degree fuzzy transform: Application to stationary processes and noise reduction. In: Kacprzyk, J., et al. (eds.) Advances in Fuzzy Logic and Technology 2017, vol. 3, pp. 1–12. Springer (2018)

    Google Scholar 

  18. Nguyen, L., Novák, V.: Filtering out high frequencies in time series using F-transform with respect to raised cosine generalized uniform fuzzy partition. In: Proc. Int. Conference FUZZ-IEEE 2015. IEEE Computer Society, CPS, Istanbul (2015)

    Google Scholar 

  19. Nguyen, L., Novák, V.: Trend-cycle forecasting based on new fuzzy techniques. In: Proc. Int. Conference FUZZ-IEEE 2017, pp. 1–6. Naples, Italy (2017)

    Google Scholar 

  20. Nguyen, L., Holčapek, M., Novák, V.: Multivariate fuzzy transform of complex-valued functions determined by monomial basis. Soft computing, 3641–3658 (2017)

    Google Scholar 

  21. Nguyen, L., Mirshahi, S., Novák, V.: Trend-cycle estimation using fuzzy transform and its application for identifying of bull and bear phases in markets. Intell. Syst. Account. Finance Manag. 27, 111–124 (2020). https://doi.org/10.1002/isaf.1473

    Article  Google Scholar 

  22. Novák, V.: Perception-based logical deduction. In: Reusch, B. (ed.) Computational Intelligence, Theory and Applications, pp. 237–250. Springer, Berlin (2005)

    Chapter  Google Scholar 

  23. Novák, V.: Mathematical fuzzy logic in modeling of natural language semantics. In: Wang, P., Ruan, D., Kerre, E. (eds.) Fuzzy Logic – A Spectrum of Theoretical & Practical Issues, pp. 145–182. Elsevier, Berlin (2007)

    Google Scholar 

  24. Novák, V.: A comprehensive theory of trichotomous evaluative linguistic expressions. Fuzzy Sets Syst. 159(22), 2939–2969 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  25. Novák, V.: A formal theory of intermediate quantifiers. Fuzzy Sets Syst. 159(10), 1229–1246 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  26. Novák, V.: Linguistic characterization of time series. Fuzzy Sets Syst. 285, 52–72 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  27. Novák, V.: Mining information from time series in the form of sentences of natural language. Int. J. Approx. Reason. 78, 192–209 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  28. Novák, V.: Detection of structural breaks in time series using fuzzy techniques. Int. J. Fuzzy Logic Intell. Syst. 18(1), 1–12 (2018)

    Article  Google Scholar 

  29. Novák, V.: Fuzzy vs. probabilistic techniques in time series analysis. In: Anh, L., Dong, L., Kreinovich, V., Thach, N. (eds.) Econometrics for Financial Applications, pp. 213–234. Springer, Berlin (2018)

    Chapter  Google Scholar 

  30. Novák, V., Lehmke, S.: Logical structure of fuzzy IF-THEN rules. Fuzzy Sets Syst. 157, 2003–2029 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  31. Novák, V., Mirshahi, S.: On the similarity and dependence of time series. MDPI Mathematics 9(5), 550–563 (2021). https://doi.org/0.3390/math9050550. http://www.mdpi.com/2227-7390/9/5/550

  32. Novák, V., Pavliska, V.: Time series: how unusual local behavior can be recognized using fuzzy modeling methods. In: Kreinovich, V. (ed.) Statistical and Fuzzy Approaches to Data Processing, with Applications to Econometrics and Other Areas, pp. 157–177. Springer, Berlin (2021)

    Chapter  MATH  Google Scholar 

  33. Novák, V., Perfilieva, I.: On the semantics of perception-based fuzzy logic deduction. Int. J. Intell. Syst. 19, 1007–1031 (2004)

    Article  MATH  Google Scholar 

  34. Novák, V., Perfilieva, I., Dvořák, A.: Insight into Fuzzy Modeling. Wiley, Hoboken, NJ (2016)

    Book  MATH  Google Scholar 

  35. Novák, V., Perfilieva, I., Holčapek, M., Kreinovich, V.: Filtering out high frequencies in time series using F-transform. Information Sciences 274, 192–209 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  36. Panigrahi, S., Behera, H.: Fuzzy time series forecasting: A survey. In: Behera, H., Nayak, J., Naik, B., Pelusi, D. (eds.) Computational Intelligence in Data Mining. pp. 641–651. Springer Singapore, Singapore (2020)

    Chapter  Google Scholar 

  37. Perfilieva, I.: Fuzzy transforms: theory and applications. Fuzzy Sets Syst. 157, 993–1023 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  38. Perfilieva, I., Adamczyk, D.: Features as keypoints and how fuzzy transforms retrieve them. In: Rojas, I., Joya, G., Català, A. (eds.) Advances in Computational Intelligence, IWANN 2021, vol. 12862. Springer, Cham (2021)

    Google Scholar 

  39. Perfilieva, I., Daňková, M., Bede, B.: Towards a higher degree F-transform. Fuzzy Sets Syst. 180, 3–19 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  40. Preuss, P., Puchstein, R., Detter, H.: Detection of multiple structural breaks in multivariate time series. J. Am. Stat. Assoc. 110, 654–668 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  41. Said, A., Taskaya-Temizel, T., Khurshid, A.: Summarizing time series: Learning patterns in ‘Volatile’ series. In: Yang, Z., Yin, H., Everson, R. (eds.) Intelligent Data Engineering and Automated Learning? IDEAL 2004, pp. 523–532. Lecture Notes in Computer Science. Springer, Berlin, Heidelberg (2004)

    Google Scholar 

  42. Song, Q., Chisom, B.: Forecasting enrollments with fuzzy time series - Part I. Fuzzy Sets Syst. 54, 1–9 (1993)

    Article  Google Scholar 

  43. Štěpnička, M., Burda, M., Štěpničková, L.: Fuzzy rule base ensemble generated from data by linguistic associations mining. Fuzzy Sets Syst. 285, 140–161 (2016)

    Article  MathSciNet  Google Scholar 

  44. Truong, P., Novák, V.: An improved forecasting and detection of structural breaks in time series using fuzzy techniques. In: Rojas, I. (ed.) Contribution to Statistics. Springer (2022)

    Google Scholar 

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Correspondence to Vilém Novák .

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Novák, V., Perfilieva, I. (2023). Nonstatistical Methods for Analysis, Forecasting, and Mining Time Series. In: Valenzuela, O., Rojas, F., Herrera, L.J., Pomares, H., Rojas, I. (eds) Theory and Applications of Time Series Analysis and Forecasting. ITISE 2021. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-031-14197-3_5

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