International Journal of Fuzzy Systems

, Volume 20, Issue 3, pp 729–740 | Cite as

A Novel Stochastic Seasonal Fuzzy Time Series Forecasting Model

  • Hilal GuneyEmail author
  • Mehmet Akif Bakir
  • Cagdas Hakan Aladag


Fuzzy time series approach has been widely used to analyze real-world time series in recent years since using this approach has some important advantages. Various fuzzy time series models have been proposed in the literature in order to reach better forecasting results. A few of these models have been suggested to forecast seasonal time series and called as seasonal fuzzy time series. In this study, a new seasonal fuzzy time series forecasting model based on Markov chain transition matrix is proposed. In the proposed approach, fuzzy inference process is performed by using transition probabilities. Therefore, fuzzy time series approach proposed in this study is the first stochastic seasonal fuzzy time series method in the literature. To show the forecasting performance of the proposed method, it is applied to two real-world time series: the quarterly U.S. beer production and the number of foreign tourists visiting Turkey. As a result of the implementation, it is observed that the proposed method produces accurate forecasting results for both time series.


Forecasting Markov chain Seasonal fuzzy time series Seasonality Transition matrix 


  1. 1.
    Aladag, C.H.: Using artificial neural networks in fuzzy time series analysis. In: Zadeh, L.A., et al. (eds.) Recent Developments and New Directions in Soft Computing, Studies in Fuzziness and Soft Computing, vol. 317, pp. 443–451. Springer, Switzerland (2014). doi: 10.1007/978-3-319-06323-2_28. ISBN 978-3-319-06322-5CrossRefGoogle Scholar
  2. 2.
    Aladag, C.H., Egrioglu, E.: Advanced time series forecasting methods. In: Aladag, C.H., Egrioglu, E. (eds.) Advances in Time Series Forecasting, pp. 3–10. Bentham Science Publishers Ltd., Sharjah (2012). ISBN 978-1-60805-373-5CrossRefGoogle Scholar
  3. 3.
    Chen, S.M.: Forecasting enrollments based on fuzzy time series. Fuzzy Sets Syst. 81, 311–319 (1996)CrossRefGoogle Scholar
  4. 4.
    Cheng, C.H., Chen, T.L., Teoh, H.J., Chiang, C.H.: Fuzzy time series based on adaptive expectation model for TAIEX forecasting. Expert Syst. Appl. 34, 1126–1132 (2008)CrossRefGoogle Scholar
  5. 5.
    Egrioğlu, E., Aladag, C.H., Yolcu, U., Basaran, M.A., Uslu, V.R.: A new hybrid approach based on SARIMA and partial high order bivariate fuzzy time series forecasting model. Expert Syst. Appl. 36, 7424–7434 (2009)CrossRefGoogle Scholar
  6. 6.
    Egrioglu, E., Aladag, C.H., Yolcu, U.: Fuzzy time series forecasting with a novel hybrid approach combining fuzzy c-means and neural networks. Expert Syst. Appl. 40(3), 854–857 (2013)CrossRefGoogle Scholar
  7. 7.
    Huarng, K.: Effective lengths of intervals to improve forecasting in fuzzy time series. Fuzzy Sets Syst. 123, 387–394 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Huarng, K.: Heuristic models of fuzzy time series for forecasting. Fuzzy Sets Syst. 123(3), 369–386 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Huarng, K.: Ratio-based lengths of intervals to improve fuzzy time series forecasting. IEEE Trans. Syst. Man Cybern. PartB: Cybern. 36, 328–340 (2006)CrossRefGoogle Scholar
  10. 10.
    Song, Q., Chissom, B.S.: Fuzzy time series and its models. Fuzzy Sets Syst. 54, 227–269 (1993)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Song, Q., Chissom, B.S.: Forecasting enrollments with fuzzy time series-Part I. Fuzzy Sets Syst. 54, 1–10 (1993)CrossRefGoogle Scholar
  12. 12.
    Song, Q.: Seasonal forecasting in fuzzy time series. Fuzzy Sets Syst. 107, 235–236 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Tsaur, R.C.: A fuzzy time series-Markov chain model with an application to forecast the exchange rate between the Taiwan and US dolar. Int. J. Innov. Comput. Inf. Control 8, 1349–4198 (2011)Google Scholar
  14. 14.
    Tseng, F.M., Tzeng, G.H.: A fuzzy seasonal ARIMA model for forecasting. Fuzzy Sets Syst. 126, 367–376 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Wei, W.W.S.: Time Series Analysis Univariate and Multivariate Methods, 1–2, pp. 174–180. Addison-Wesley, Boston (1989)Google Scholar
  16. 16.
    Yolcu, U., Egrioğlu, E., Uslu, V.R., Basaran, M.A., Aladag, C.H.: A new approach for determining the length of intervals for fuzzy time series. Appl. Soft Comput. 9, 647–651 (2009)CrossRefzbMATHGoogle Scholar
  17. 17.
    Yu, H.K.: Weighted fuzzy time series models for TAIEX forecasting. Phys. A 624, 609–624 (2005)CrossRefGoogle Scholar
  18. 18.
    Yu, H.K.: A refined fuzzy time series model for forecasting. Physica A 346, 657–681 (2005)CrossRefGoogle Scholar
  19. 19.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)CrossRefzbMATHGoogle Scholar

Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Hilal Guney
    • 1
    Email author
  • Mehmet Akif Bakir
    • 2
  • Cagdas Hakan Aladag
    • 3
  1. 1.Narman Technical Science CollegeAtatürk UniversityErzurumTurkey
  2. 2.Department of Statistics, Faculty of ScienceGazi UniversityAnkaraTurkey
  3. 3.Department of Statistics, Faculty of ScienceHacettepe UniversityAnkaraTurkey

Personalised recommendations