Abstract
Non-probabilistic forecasting methods are commonly used in various scientific fields. Fuzzy-time-series methods are well-known non-probabilistic and nonlinear forecasting methods. Although these methods can produce accurate forecasts, linear autoregressive models can produce forecasts that are more accurate than those produced by fuzzy-time-series methods for some real-world time series. It is well known that hybrid forecasting methods are useful techniques for forecasting time series and that they have the capabilities of their components. In this study, a new hybrid forecasting method is proposed. The components of the new hybrid method are a high-order fuzzy-time-series forecasting model and autoregressive model. The new hybrid forecasting method has a network structure and is called a fuzzy-time-series network (FTS-N). The fuzzy c-means method is used for the fuzzification of time series in FTS-N, which is trained by particle swarm optimization. Istanbul Stock Exchange daily data sets from 2009 to 2013 and the Taiwan Stock Exchange Capitalization Weighted Stock Index data sets from 1999 to 2004 were used to evaluate the performance of FTS-N. The applications reveal that FTS-N produces more accurate forecasts for the 11 real-world time-series data sets.
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References
Box GEP, Jenkins GM (1976) Time series analysis: Forecasting and control. Holdan-Day, San Francisco, CA
Zadeh LA (1965) Fuzzy sets. Inform and Control 8:338–353
Mamadani EH, Assilian S (1975) An experiment in linguistic synthesis with a fuzzy logic controller. Int J Man Math Stat 7(1):1–13
Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE Trans On system, Man and Cybern 15(1):116–132
Jang JSR (1993) ANFIS: Adaptive network based fuzzy inference system. IEEE Trans On system, Man and Cybern 23(3):665–685
Turksen B (2008) Fuzzy function with LSE. Appl Soft Comput 8:1178–1188
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
Zarandi MHF, Zarinbal M, Ghanbari N, Turksen IB (2013) A new fuzzy functions model tuned by hybridizing imperialist competitive algorithm and simulated annealing. Application: stock price prediction. Inf Sci 222(11):213–228
Song Q, Chissom BS (1993a) Fuzzy time series and its models. Fuzzy Sets Syst 54:269–277
Song Q, Chissom BS (1993b) Forecasting enrollments with fuzzy time series - Part I. Fuzzy Sets Syst 54:1–10
Song Q, Chissom BS (1994) Forecasting enrollments with fuzzy time series - Part II. Fuzzy Sets Syst 62(1):1–8
Chen SM (1996) Forecasting enrollments based on fuzzy time-series. Fuzzy Sets Syst 81:311–319
Huarng K, Yu HK (2006) The application of neural networks to forecast fuzzy time series. Physica A 363:481–491
Aladag CH, Basaran MA, Egrioglu E, Yolcu U, Uslu VR (2009) Forecasting in high order fuzzy time series by using neural networks to define fuzzy relations. Expert Syst Appl 36:4228–4231
Davari S, Zarandi MHF, Turksen IB (2009) An Improved fuzzy time series forecasting model based on particle swarm intervalization. In: The 28 th North American Fuzzy Information Processing Society Annual Conferences (NAFIPS 2009). Cincinnati, Ohio, USA, June 14-17
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
Kuo IH, Horng SJ, Chen YH, Run RS, Kao TW, Chen RJ, Lai JL, Lin TL (2010) Forecasting TAIFEX based on fuzzy time series and particle swarm optimization. Expert Syst Appl 37:1494–1502
Park JI, Lee DJ, Song CK, Chun MG (2010) TAIFEX and KOSPI 200 forecasting based on two factors high order fuzzy time series and particle swarm optimization. Expert Syst Appl 37:959–967
Hsu LY, Horng SJ, Kao TW, Chen YH, Run RS, Chen RJ, Lai JL, Kuo IH (2010) Temperature prediction and TAIFEX forecasting based on fuzzy relationships and MTPSO techniques. Expert Syst Appl 37:2756–2770
Huang YL, Horng SJ, Kao TW, Run RS, Lai JL, Chen RJ, Kuo IH, Khan MK (2011) An improved forecasting model based on the weighted fuzzy relationship matrix combined with a PSO adaptation for enrollments. Int J Innov Comput, Inf Control 7(8):4027–4046
Aladag CH, Yolcu U, Egrioglu E, Dalar AZ (2012) A new time invariant fuzzy time series forecasting method based on particle swarm optimization. Appl Soft Comput 12:3291–3299
Egrioglu E, Yolcu U, Aladag CH, Kocak C (2013) An ARMA type fuzzy time series forecasting method based on particle swarm optimization. Math Probl Eng, Article ID 935815, 12 pages. doi:10.1155/2013/935815
Chen SM, Chung NY (2006) Forecasting enrolments using high order fuzzy time series and genetic algorithms. Int J Intell Syst 21:485–501
Lee LW, Wang LH, Chen SM, Leu YH (2006) Handling forecasting problems based on two factor high-order fuzzy time series. IEEE Trans on Fuzzy Syst 14(3):468–477
Egrioglu E (2012) A new time invariant fuzzy time series forecasting method based on genetic algorithm. Adv Fuzzy Syst, Article ID 785709, 6 pages,
Uslu VR, Bas E, Yolcu U, Egrioglu E (2013) A fuzzy time series approach based on weights determined by the number of recurrences of fuzzy relations. Swarm and Evol Comput, Accepted Manuscript. doi:10.1016/j.swevo.2013.10.004
Bas E, Uslu VR, Yolcu U, Egrioglu E (2014) A modified genetic algorithm for forecasting fuzzy time series. Appl Intell, Accepted Paper. doi:10.1007/s10489-014-0529-x
Yolcu U, Yolcu OC, Aladag CH, Egrioglu E (2014) An enhanced fuzzy time series forecasting method based on artificial bee colony algorithm. J. Intell Fuzzy Syst, Accepted Paper. doi:10.3233/IFS-130933
Egrioglu E, Aladag CH, Yolcu U, Uslu VR, Basaran MA (2009a) A new approach based on artificial neural networks for high order multivariate fuzzy time series. Expert Syst Appl 36:10589–10594
Egrioglu E, Aladag CH, Yolcu U, Basaran MA, Uslu VR (2009b) A new hybrid approach based on Sarima and partial high order bivariate fuzzy time series forecasting model. Expert Syst Appl 36:7424–7434
Egrioglu E, Uslu VR, Yolcu U, Basaran MA, Aladag CH (2009c) A new approach based on artificial neural networks for high order bivariate fuzzy time series. Appl Soft Comput 58:265–273
Aladag CH (2013) Using multiplicative neuron model to establish fuzzy logic relationships. Expert Syst Appl 40(3):850–853
Huarng K, Yu HK, Hsu YW (2007) A multivariate heuristic model for fuzzy time-series forecasting. IEEE Trans Syst, Man Cybern B ,Cybern 37(4):836–846
Yu THK, Huarng KH (2008) A bivariate fuzzy time series model to forecast the TAIEX. Expert Syst Appl 34(4):2945–2952
Chen SM, Chang YC (2010) Multi-variable fuzzy forecasting based on fuzzy clustering and fuzzy rule interpolation techniques. Inf Sci 180(24):4772–4783
Chen SM, Chen CD (2011) TAIEX forecasting based on fuzzy time series and fuzzy variation groups. IEEE Trans Fuzzy Syst 19(1):1–12
Chen SM, Chu HP, Sheu TW (2012) TAIEX forecasting using fuzzy time series and automatically generated weights of multiple factors. IEEE Trans On Syst, Man, and Cybern—Part A: Syst and Humans 42(7):1485–1495
Tseng FM, Yu HC, Tzeng GH (2002) Combining neural network model with seasonal time series ARIMA model. Technol Forecast Soc Chang 69:71–87
Zhang G (2003) Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing 50:159–175
BuHamra S, Smaoui N, Gabr M (2003) The Box-Jenkins analysis and neural networks: prediction and time series modeling. Appl. Math Model 27:805–815
Pai PF, Lin CS (2005) A hybrid ARIMA and support vector machines model in stock price forecasting. Omega 33(7):497– 505
Wang W, Van Gelder PHAJM, Vrijling JK, Ma J (2006) Forecasting daily stream flow using hybrid ANN models. J Hydrol 324:383–399
Jain A, Kumar AM (2007) Hybrid neural network models for hydrological time series forecasting. Appl Soft Comput 7:585–592
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
Aladag CH, Egrioglu E, Kadilar C (2009d) Forecasting nonlinear time series with a hybrid methodology. Appl Mathematic Lett 22:1467–1470
Lee Y-S, Tong L-I (2011) Forecasting time series using a methodology based on autoregressive integrated moving average and genetic programming. Knowl-Based Syst 24:66–72
Yolcu U, Aladag CH, Egrioglu E (2013) A new linear & nonlinear artificial neural network model for time series forecasting. Decis Support Syst. J 54:1340–1347
Bezdek JC (1981) Pattern recognition with fuzzy objective function algorithms. Plenum Press, NY
Kennedy J , Eberhart R (1995) Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks, Piscataway, NJ, USA, IEEE Press., 1995, 1942
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Bas, E., Egrioglu, E., Aladag, C.H. et al. Fuzzy-time-series network used to forecast linear and nonlinear time series. Appl Intell 43, 343–355 (2015). https://doi.org/10.1007/s10489-015-0647-0
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DOI: https://doi.org/10.1007/s10489-015-0647-0