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Fuzzy Transform in Time Series Decomposition

  • Linh NguyenEmail author
  • Vilém Novák
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1000)

Abstract

In this paper, we provide a method for applying the fuzzy transform of higher degree to time series decomposition. We assume that a time series can be decomposed into a trend-cycle, a seasonal component and an irregular fluctuation, we devote theoretical justifications for decomposing it into an additive model. Several examples are consider to demonstrate our methodology.

Notes

Acknowledgements

This work is supported by the project GA ČR No. 18-13951S.

References

  1. 1.
    Alexandrov, T., Bianconcini, S., Dagum, E.B., Maass, P., McElroy, T.S.: A review of some modern approaches to the problem of trend extraction. Econom. Rev. 31(6), 593–624 (2012)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Anděl, J.: Statistical Analysis of Time Series. SNTL, Praha (1976). (in Czech)Google Scholar
  3. 3.
    Dagum, E.B.: The X-II-ARIMA seasonal adjustment method. Catalogue No. 12-564E (1980)Google Scholar
  4. 4.
    Godolphin, E., Triantafyllopoulos, K.: Decomposition of time series models in state space form. Comput. Stat. Data Anal. 50, 2232–2246 (2006)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Hamilton, J.D.: Time Series Analysis. Princeton University Press, Princeton (1994)zbMATHGoogle Scholar
  6. 6.
    Holčapek, M., Nguyen, L.: Trend-cycle estimation using fuzzy transform of higher degree. Iran. J. Fuzzy Syst. 15(7), 23–54 (2018)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Holčapek, M., Nguyen, L., Tichý, T.: Polynomial alias higher degree fuzzy transform of complex-valued functions. Fuzzy Sets Syst. 342, 1–31 (2017)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Holčcapek, M., Nguyen, L.: Suppression of high frequencies in time series using fuzzy transform of higher degree. In: 16th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2016, Eindhoven, The Netherlands, pp. 705–716 (2016)Google Scholar
  9. 9.
    Nguyen, L., Holčapek, M., Novák, V.: Multivariate fuzzy transform of complex-valued functions determined by monomial basis. Soft Comput. 21(13), 3641–3658 (2017)CrossRefGoogle Scholar
  10. 10.
    Nguyen, L., Holčcapek, M.: Higher degree fuzzy transform: application to stationary processes and noise reduction. In: Advances in Fuzzy Logic and Technology 2017, EUSFLAT 2017, pp. 1–12. Springer, Warsaw (2017)Google Scholar
  11. 11.
    Nguyen, L., Novák, V.: Forecasting seasonal time series based on fuzzy techniques. Fuzzy Sets Syst. (2018).  https://doi.org/10.1016/j.fss.2018.09.010MathSciNetCrossRefGoogle Scholar
  12. 12.
    Novák, V.: Linguistic characterization of time series. Fuzzy Sets Syst. 285, 52–72 (2016)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Novák, V.: Mining information from time series in the form of sentences of natural language. Int. J. Approximate Reasoning 78, 192–209 (2016)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Novák, V., Perfilieva, I., Holčapek, M., Kreinovich, V.: Filtering out high frequencies in time series using f-transform. Inf. Sci. 274, 192–209 (2014)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Novák, V., Perfilieva, I., Romanov, A., Yarushkina, N.: Time series grouping and trend forecast using f\(^1\)-transform and fuzzy natural logic. In: Marco se Moraes, R., Kerre, E.E., dos Santos Machado, L., Lu, J. (eds.) Decision Making and Soft Computing, pp. 143–148. World Scientific (2014)Google Scholar
  16. 16.
    Novák, V., Štépnička, M., Dvořák, A., Perfilieva, I., Pavliska, V., Vavříčková, L.: Analysis of seasonal time series using fuzzy approach. Int. J. Gen. Syst. 39, 305–328 (2010)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Perfilieva, I.: Fuzzy transforms: theory and applications. Fuzzy Sets Syst. 157, 993–1023 (2006)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Perfilieva, I., Daňková, M., Bede, B.: Towards a higher degree f-transform. Fuzzy Sets Syst. 180, 3–19 (2011)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Theodosiou, M.: Forecasting monthly and quarterly time series using STL decomposition. Int. J. Forecast. 27, 1178–1195 (2011)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute for Research and Applications of Fuzzy Modelling, NSC IT4InnovationsUniversity of OstravaOstrava 1Czech Republic

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