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Recurrent type-1 fuzzy functions approach for time series forecasting

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Abstract

Forecasting the future values of a time series is a common research topic and is studied using probabilistic and non-probabilistic methods. For probabilistic methods, the autoregressive integrated moving average and exponential smoothing methods are commonly used, whereas for non-probabilistic methods, artificial neural networks and fuzzy inference systems (FIS) are commonly used. There are numerous FIS methods. While most of these methods are rule-based, there are a few methods that do not require rules, such as the type-1 fuzzy function (T1FF) approach. While it is possible to encounter a method such as an autoregressive (AR) model integrated with a T1FF, no method that includes T1FF and the moving average (MA) model in one algorithm has yet been proposed. The aim of this study is to improve forecasting by taking the disturbance terms into account. The input dataset is organized using the following variables. First, the lagged values of the time series are used for the AR model. Second, a fuzzy c-means clustering algorithm is used to cluster the inputs. Third, for the MA, the residuals of fuzzy functions are used. Hence, AR, MA, and the degree of memberships of the objects are included in the input dataset. Because the objective function is not derivative, particle swarm optimization is preferable for solving it. The results on several datasets show that the proposed method outperforms most of the methods in literature.

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References

  1. Aladag CH, Yolcu U, Egrioglu E, Dalar AZ (2012) A new time invariant fuzzy time series method based on particle swarm optimization. Appl Soft Comput 12:3291–3299

    Article  Google Scholar 

  2. Aladag CH, Turksen IB, Dalar AZ, Egrioglu E, Yolcu U (2014) Application of type-1 fuzzy functions approach for time series forecasting. Turk J Fuzzy Syst 5(1):1–9

    Google Scholar 

  3. Bas E, Egrioglu E, Yolcu U, Aladag CH (2015) Fuzzy time series network used to forecast linear and nonlinear time series. Appl Intell 43(2):343–355

    Article  Google Scholar 

  4. Bas E, Uslu VR, Yolcu U, Egrioglu E (2014) A modified genetic algorithm for fuzzy time series to find the optimal interval length. Appl Intell 42(2):453–463

    Article  Google Scholar 

  5. Beyhan S, Alci M (2010) Fuzzy functions based arx model and new fuzzy basis function models for nonlinear system identification. Appl Soft Comput 10:439–444

    Article  Google Scholar 

  6. BIST100 (2015) Istanbul Stock Exchange Index Dataset. http://www.borsaistanbul.com/veriler/gecmise-donuk-veri-satisi. Accessed 5 November 2015

  7. Box GEP, Jenkins GM (1976) Time series analysis: forecasting and control. Holdan-Day, San Francisco

    MATH  Google Scholar 

  8. BuHamra S, Smaoui N, Gabr M (2003) The box-Jenkins analysis and neural networks: prediction and time series modeling. Apple Math Model 27(10):805–815

    Article  MATH  Google Scholar 

  9. Catalao JPS, Pousinho HMI, Mendes VMF (2011) Hybrid wavelet PSO ANFIS approach for short term wind power forecasting in Portugal. IEEE Trans Sustain Energy 2(1):50–59

    Google Scholar 

  10. Celikyilmaz A, Turksen B (2009) Modeling uncertainty with fuzzy logic: with recent theory and applications. Springer, Berlin

    Book  MATH  Google Scholar 

  11. Chabaa S, Zeroual A, Antari J (2009), ANFIS method for forecasting internet traffic time series. In: IEEE microwave symposium

  12. Chang B (2008) Resolving the forecasting problems of overshoot and volatility clustering using ANFIS coupling nonlinear heteroscedasticity with quantum tuning. Fuzzy Set Syst 159(23):3183–3200

    Article  MathSciNet  MATH  Google Scholar 

  13. Chau KW (2006) Particle swarm optimization training algorithm for ANNs in stage prediction of Shing Mun River. J Hydrol 329:363–367

    Article  Google Scholar 

  14. Chen B, Ma Z (2009) Short-term traffic flow prediction based on ANFIS. In: IEEE communication software and networks, pp 791–793

  15. Chen D, Zhang J (2005) Time series prediction based on ensemble ANFIS. In: Proceedings of the fourth international conference on machine learning and cybermetics, pp 3552–3556

  16. Chen KY, Wang CH (2007) A hybrid SARIMA and support vector machines in forecasting the production values of the machinery industry in Taiwan. Expert Syst Appl 32(1):254–264

    Article  MathSciNet  Google Scholar 

  17. Chen SM (1996) Forecasting enrollments with fuzzy time series. Fuzzy Set Syst 81:311–319

    Article  Google Scholar 

  18. Chen SM, Chung NY (2006) Forecasting enrollments using high-order fuzzy time series and genetic algorithms. Int J Intell Syst 21:485–501

    Article  MATH  Google Scholar 

  19. Chen SM, Tanuwijaya K (2011) Multivariate fuzzy forecasting based on fuzzy time series and automatic clustering techniquesh. Expert Syst Appl 38:10594–10605

    Article  Google Scholar 

  20. Egrioglu E (2012) A new time invariant fuzzy time series forecasting method based on genetic algorithm. Adv Fuzzy Syst 2012:Article ID 785709

    MathSciNet  MATH  Google Scholar 

  21. Egrioglu E, Aladag CH, Yolcu U, Bas E (2014) A new adaptive network based fuzzy inference system for time series forecasting. Aloy J Soft Comput Appl 2:25–32

    Google Scholar 

  22. Egrioglu E, Aladag CH, Yolcu U, Uslu VR, Basaran MA (2009) A new approach based on artificial neural networks for high order multivariate fuzzy time series. Expert Syst Appl 36:10589–10594

    Article  Google Scholar 

  23. Huang CM, Huang CJ, Wang ML (2005) A particle swarm optimization to identifying the ARMAX model for short-term load forecasting. IEEE T Power Syst 20(2):1126–1133

    Article  Google Scholar 

  24. Huarng KH (2007) A multivariate heuristic model for fuzzy time-series forecasting. IEEE Trans Syst Man Cybern 37(4):836–846

    Article  Google Scholar 

  25. Huarng K, Yu HK (2006) The application of neural networks to forecast fuzzy time series. Phys A 363:481–491

    Article  Google Scholar 

  26. Jain A, Kumar AM (2007) Hybrid neural network models for hydrological time series forecasting. Appl Soft Comput 7:585–592

    Article  Google Scholar 

  27. Janacek GJ (2001) Practical time series. Arnold

  28. Jang JSR (1993) ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans Syst Man Cybern 23(3):665–685

    Article  Google Scholar 

  29. Jilani TA, Burney SMA, Ardil C (2008) Multivariate high order fuzzy time series forecasting for car road accidents. Int J Comput Int Syst 4:15–20

    Google Scholar 

  30. Kim D, Kim C (1997) Forecasting time series with genetic fuzzy predictor ensemble. IEEE Trans Fuzzy Syst 5(4):523–535

    Article  Google Scholar 

  31. Kuo IH, Horng SJ, Kao TW, Lin TL, Lee CL, Pan Y (2009) An improved method for forecasting enrollments based on fuzzy time series and particle swarm optimization. Expert Syst Appl 36:6108–6117

    Article  Google Scholar 

  32. Kuo RJ, Chen CH, Hwang YC (2001) An intelligent trading decision support system through integration of genetic algorithm based fuzzy neural network and artifical neural network. Fuzzy Set Syst 118:21–45

    Article  Google Scholar 

  33. Lee YS, Tong LI (2011) Forecasting time series using a methodology based on autoregressive integrated moving average and genetic algorithm. Knowl-Based Syst 24(1):66–72

    Article  Google Scholar 

  34. Mamdani EH, Assilian S (1975) An experiment in linguistic synthesis with a fuzzy logic controller. Int J Man Mach Stud 7(1):1–13

    Article  MATH  Google Scholar 

  35. Pai PF, Lin CS (2005) A hybrid ARIMA and support vector machines model in stock price forecasting. Omega 33(7):497–505

    Article  Google Scholar 

  36. Park FI, Lee DJ, Song CK, Chun (2010) TAIEX and KOSPI forecasting based on two-factor high-order fuzzy time series and particle swarm optimization. Expert Syst Appl 37:959–967

    Article  Google Scholar 

  37. Song Q, Chissom BS (1993) Fuzzy time series and its models. Fuzzy Set Syst 54:269–277

    Article  MathSciNet  MATH  Google Scholar 

  38. Song Q, Chissom BS (1993) Forecasting enrollments with fuzzy time series – part I. Fuzzy Set Syst 54:1–10

    Article  Google Scholar 

  39. Song Q, Chissom BS (1994) Forecasting enrollments with fuzzy time series – part II. Fuzzy Set Syst 62(1):1–8

    Article  Google Scholar 

  40. TAIEX (2015) Taiwan Stock Exchange Index Dataset. http://www.taiwanindex.com.tw/index/history/t00. Accessed 17 October 2015

  41. Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Syst Man Cybern 15(1):116–132

    Article  MATH  Google Scholar 

  42. Turksen IB (2008) Fuzzy functions with LSE. Appl Soft Comput 8(3):1178–1188

    Article  Google Scholar 

  43. Tseng FM, Yu HC, Tseng GH (2002) Combining neural network model with seasonal time series ARIMA model. Technol Forecast Soc 69:71–87

    Article  Google Scholar 

  44. Yolcu U, Aladag CH, Egrioglu E (2013) A new linear and nonlinear artificial neural network model for time series forecasting. Decis Support Syst 54(3):1340–1347

    Article  Google Scholar 

  45. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  MATH  Google Scholar 

  46. Zadeh LA (1973) Outline of a new approach to the analysis of complex systems and decision process. IEEE Trans Syst Man Cybern 3(1):28–44

    Article  MathSciNet  MATH  Google Scholar 

  47. Zhang G (2003) Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing 50:159–175

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Faculty of Economics and Administrative Sciences, Kirklareli University, Kirklareli, Turkey

    Nihat Tak

  2. Faculty of Arts and Sciences, Yildiz Technical University, Istanbul, Turkey

    Atif A. Evren

  3. Faculty of Arts and Sciences, Marmara University, Istanbul, Turkey

    Mujgan Tez

  4. Faculty of Arts and Sciences, Giresun University, Giresun, Turkey

    Erol Egrioglu

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  1. Nihat Tak
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  2. Atif A. Evren
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  3. Mujgan Tez
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  4. Erol Egrioglu
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Correspondence to Nihat Tak.

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Tak, N., Evren, A.A., Tez, M. et al. Recurrent type-1 fuzzy functions approach for time series forecasting. Appl Intell 48, 68–77 (2018). https://doi.org/10.1007/s10489-017-0962-8

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  • DOI: https://doi.org/10.1007/s10489-017-0962-8

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