A non-parametric model for fuzzy forecasting time series data. (English) Zbl 1477.62245
Summary: The time series analysis is mainly aimed at establishing a fuzzy prediction model based on a set of real-valued time series data. To achieve this goal, the present paper proposes a different strategy to convert the exact prediction into the fuzzy domain. For this purpose, a non-parametric kernel-based statistical method was suggested and discussed. In this regard, flexible right and left spreads were introduced as some parametric forms and the fuzzy prediction scheme was constructed as LR-fuzzy numbers. A hybrid algorithm was also developed to evaluate the optimal values of the autoregressive order, bandwidth, and the unknown parameters of left and right spread. Four popular time series data sets were employed to examine the proposed algorithm. The accuracy of the proposed method was also evaluated in terms of some performance measures through its comparison with some common fuzzy time series models. The results indicated that the proposed fuzzy time series model is potentially effective in forecasting fuzzy time series data in real applications.
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62M20 | Inference from stochastic processes and prediction |
| 62M86 | Inference from stochastic processes and fuzziness |
Keywords:
nonparametric time series; fuzzy time series data; kernel method; optimal bandwidth; autoregressive order; defuzzified criterionReferences:
| [1] | Abhishekh, G.; Gautam, SS; Singh, SR, A refined weighted method for forecasting based on type-2 fuzzy time series, Int J Model Simul, 38, 180-188 (2018) |
| [2] | Aladag, CH, Using multiplicative neuron model to establish fuzzy logic relationships, Expert Syst Appl, 40, 850-853 (2013) |
| [3] | Bas, E.; Yolcu, U.; Egrioglu, E., Intuitionistic fuzzy time series functions approach for time series forecasting, Gran Comput (2020) · Zbl 1436.62455 · doi:10.1007/s41066-020-00220-8 |
| [4] | Bisht, K.; Kumar, S., Fuzzy time series forecasting method based on hesitant fuzzy sets, Expert Syst Appl, 64, 557-568 (2016) |
| [5] | Bose, M.; Mali, K., A novel data partitioning and rule selection technique for modeling high-order fuzzy time series, Appl Soft Comput, 63, 87-96 (2018) |
| [6] | Bose, M.; Mali, K., Designing fuzzy time series forecasting models: a survey, Int J Approx Reas, 111, 78-99 (2019) · Zbl 1466.62396 |
| [7] | Bosq, D., Nonparametric statistics for stochastic process (1996), New York: Springer, New York · Zbl 0857.62081 |
| [8] | Box, GEP; Jenkins, GM, Time series analysis: forecasting and control (1976), San Francisco: Holden-Day, San Francisco · Zbl 0363.62069 |
| [9] | Brockwell, PJ; Davies, RA, Time series: theory and methods (1991), New York: Springer-Verlag, New York · Zbl 0709.62080 |
| [10] | Bulut, E., Modeling seasonality using the fuzzy integrated logical forecasting (FILF) approach, Expert Syst Appl, 41, 1806-1812 (2014) |
| [11] | Chen, SM, Forecasting enrollments based on fuzzy time series, Fuzzy Sets Syst, 81, 311-319 (1996) |
| [12] | Chen, MY, A high-order fuzzy time series forecasting model for internet stock trading, Future Gener Comput Syst, 37, 461-467 (2014) |
| [13] | Chen, MY; Chen, BT, A hybrid fuzzy time series model based on granular computing for stock price forecasting, Inf Sci, 294, 227-241 (2015) |
| [14] | Chen, SM; Tanuwijaya, K., Multivariate fuzzy forecasting based on fuzzy time series and automatic clustering techniques, Expert Syst Appl, 38, 10594-10605 (2011) |
| [15] | Cheng, SH; Chen, SM; Jian, WS, Fuzzy time series forecasting based on fuzzy logical relationships and similarity measures, Inf Sci, 327, 272-287 (2016) · Zbl 1458.62237 |
| [16] | Chou, MT, Long term predictive value interval with the fuzzy time series, J Mar Sci Tech, 19, 509-513 (2011) |
| [17] | Duru, O.; Bulut, E., A non-linear clustering method for fuzzy time series: histogram damping partition under the optimized cluster paradox, Appl Soft Comput, 24, 742-748 (2014) |
| [18] | Efendi, R.; Ismail, Z.; Deris, MM, A new linguistic out-sample approach of fuzzytime series for daily forecasting of Malaysian electricity load demand, Appl Soft Comput, 28, 422-430 (2015) |
| [19] | Efromovich, S., Nonparametric curve estimation: methods, theory and applications (1999), New York: Springer, New York · Zbl 0935.62039 |
| [20] | Egrioglu, E.; Fildes, R.; Bas, E., Recurrent fuzzy time series functions approaches for forecasting, Granul Comput (2021) · doi:10.1007/s41066-021-00257-3 |
| [21] | Gangwar, SS; Kumar, S., Probabilistic and intuitionistic fuzzy sets based method for fuzzy time series forecasting, Cybern Syst, 45, 349-361 (2014) · Zbl 1331.93128 |
| [22] | Gasser T, Muller HG (1979) Kernel estimation of regression functions. In: Gasser T, Rosenblatt M (eds) Smoothing techniques for curve estimation. Lecture Notes in Mathematics, vol 757. Springer, Berlin, Heidelberg. doi:10.1007/BFb0098489 · Zbl 0418.62033 |
| [23] | Gautam, ASS; Singh, SR, A Score function-based method of forecasting using intuitionistic fuzzy time series, New Math Nat Comput (NMNC), 14, 91-111 (2018) |
| [24] | Gupta, KKV; Kumar, S.; Mandal, J.; Bhattacharyya, D.; Auluck, N., Fuzzy time series forecasting method using probabilistic fuzzy sets, Advanced computing and communication technologies. Advances in intelligent systems and computing (2019), Singapore: Springer, Singapore · doi:10.1007/978-981-13-0680-8-4 |
| [25] | Gupta, KK; Kumar, S., A novel high-order fuzzy time series forecasting method based on probabilistic fuzzy sets, Gran Comput, 4, 699-713 (2019) |
| [26] | Hall, P.; Jing, B., On sample reuse methods for dependent data, J R Stat Soc Ser B, 58, 727-737 (1996) · Zbl 0860.62037 |
| [27] | Hardle, W., Applied nonparametric regression (1990), New York: Cambridge University Press, New York · Zbl 0714.62030 |
| [28] | Hesamian, G.; Shams, M., Parametric testing statistical hypotheses for fuzzy random variables, Soft Comput, 20, 1537-1548 (2016) · Zbl 1373.62118 |
| [29] | Hesamian, G.; Akbari, MG, A semi-parametric model for time series based on fuzzy data, IEEE Trans Fuzzy Syst, 26, 2953-2966 (2018) |
| [30] | Holicapek M, Nguyen L (2016) 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, 2016, pp 705-716 · Zbl 1460.62146 |
| [31] | Huang, YL; Horng, SJ; He, M.; Fan, P.; Kao, TW; Khan, MK; Lai, JL; Kuo, IH, A hybrid forecasting model for enrollments based on aggregated fuzzy time series and particle swarm optimization, Expert Syst Appl, 38, 8014-8023 (2011) |
| [32] | Huarng, K., Effective lengths of intervals to improve forecasting in fuzzy time series, Fuzzy Sets Syst, 123, 387-394 (2001) · Zbl 0992.91077 |
| [33] | Hwang, JR; Chen, SM; Lee, CH, Handling forecasting problems using fuzzy time series, Fuzzy Sets Syst, 100, 217-228 (1998) |
| [34] | Ilieva, G., Fuzzy supervised multi-period time series forecasting, Cybern Inf Technol, 19, 74-86 (2019) |
| [35] | Joshi, BP; Kumar, S., Intuitionistic fuzzy sets based method for fuzzy time series forecasting, Cybern Syst, 43, 34-47 (2012) · Zbl 1332.62377 |
| [36] | Jung, HY; Choi, SH, Time series using fuzzy logic, Commun Korean Stat Soc, 15, 517-530 (2008) |
| [37] | Kocak, C., ARMA \((p, q)\)-type high order fuzzy time series forecast method based on fuzzy logic relations, Appl Soft Comput, 58, 92-103 (2017) |
| [38] | Kumar, S.; Gangwar, SS, A fuzzy time series forecasting method induced by intuitionistic fuzzy sets, Int J Model Simul Sci Comput, 6, 4, 155 (2015) |
| [39] | Kumar, S.; Gangwar, SS, Intuitionistic fuzzy time series: an approach for handling nondeterminism in time series forecasting, IEEE Trans Fuzzy Syst, 24, 1270-1281 (2018) |
| [40] | Lee, KH, First course on fuzzy theory and applications (2005), Berlin: Springer-Verlag, Berlin · Zbl 1063.94129 |
| [41] | Lee, HS; Chou, MT, Fuzzy forecasting based on fuzzy time series, Int J Comput Math, 81, 781-789 (2004) · Zbl 1093.62574 |
| [42] | Lee, WJ; Jung, HY; Yoon, JH; Choi, SH, A novel forecasting method based on F-transform and fuzzy time series, Int J Fuzzy Syst, 19, 1793-1802 (2017) |
| [43] | Li, ST; Kuo, SC; Cheng, YC; Chen, CC, Deterministic vector long-term forecasting for fuzzy time series, Fuzzy Sets Syst, 161, 1852-1870 (2010) · Zbl 1191.62161 |
| [44] | Liu, HT, An improved fuzzy time series forecasting method using trapezoidal fuzzy numbers, Fuzzy Opt Decis Making, 6, 63-80 (2007) · Zbl 1105.62092 |
| [45] | Nguyen, L.; Novák, V., Forecasting seasonal time series based on fuzzy techniques, Fuzzy Sets Syst, 361, 114-129 (2019) · Zbl 1426.62277 |
| [46] | Palma W (2016) Time series analysis. John Wiley & Sons · Zbl 1401.62003 |
| [47] | Pathak, HK; Singh, P., A new bandwidth interval based forecasting method for enrollments using fuzzy time series, Appl Math, 2, 504-507 (2011) |
| [48] | Peng, HW; Wu, SF; Wei, CC; Lee, SJ, Time series forecasting with a neuro-fuzzy modeling scheme, Appl Soft Comput, 32, 481-493 (2015) |
| [49] | Sadaei, HJ; Enayatifar, R.; Abdullah, AH; Gani, A., Short-term load forecasting using a hybrid model with a refined exponentially weighted fuzzy time series and an improved harmony search, Int J Electr Power Energy Syst, 62, 118-129 (2014) |
| [50] | Sadaei, HJ; Enayatifar, R.; Lee, MH; Mahmud, M., A hybrid model based on differential fuzzy logic relationships and imperialist competitive algorithm for stock market forecasting, Appl Soft Comput, 40, 132-149 (2016) |
| [51] | Sadaei, HJ; Enayatifar, R.; Guimaraes, FG; Mahmud, M.; Alzamil, ZA, Combining ARFIMA models and fuzzy time series for the forecast of Longmemory time series, Neurocomputing, 175, 782-796 (2016) |
| [52] | Sadaei, HJ; Guimaraes, FG; da Silva, CJ; Lee, MH; Eslami, T., Short-term load forecasting method based on fuzzy time series, seasonality and long memory process, Int J Approx Reason, 83, 196-217 (2017) · Zbl 1407.62325 |
| [53] | Shumway RH, Stoffer DS (2011) Time series analysis and its applications. With R Example. 4th edition, Springer, Berlin · Zbl 1276.62054 |
| [54] | Silva, PCL; Sadaei, HJ; Ballini, R.; Guimares, FG, Probabilistic forecasting with fuzzy time series, IEEE Trans Fuzzy Syst, 14, 2019 (2020) · doi:10.1109/TFUZZ.2019.2922152 |
| [55] | Silverman BW (1986) Density Estimation for Statistics and Data Analysis. Chapman and Hall, London · Zbl 0617.62042 |
| [56] | Simonoff, J., Smoothing methods in statistics (1996), New York: Springer, New York · Zbl 0859.62035 |
| [57] | Song, Q.; Chissom, BS, Forecasting enrollments with fuzzy time series—part I, Fuzzy Sets Syst, 54, 1-9 (1993) |
| [58] | Song, Q.; Chissom, BS, Fuzzy time series and its models, Fuzzy Sets Syst, 54, 269-277 (1993) · Zbl 0792.62087 |
| [59] | Talarposhtia, FM; Hossein, JS; Rasul, E.; Guimaraesc, FG; Mahmud, M.; Eslami, T., Stock market forecasting by using a hybrid model of exponential fuzzy time series, Int J Approx Reason, 70, 79-98 (2016) · Zbl 1414.91426 |
| [60] | Tinh, NV, Enhanced forecasting accuracy of fuzzy time series model based on combined fuzzy C-mean clustering with particle swam optimization, Int J Comput Intell Appl, 19, 1-26 (2020) |
| [61] | Torbat, S.; Khashei, M.; Bijari, M., A hybrid probabilistic fuzzy ARIMA model for consumption forecasting in commodity markets, Econ Anal Policy, 58, 22-31 (2018) |
| [62] | Uslu, VR; Bas, E.; Yolcu, U.; Egrioglu, E., A fuzzy time series approach based on weights determined by the number of recurrences of fuzzy relations, Swarm Evol Comput, 15, 19-26 (2014) |
| [63] | Vovan, T., An improved fuzzy time series forecasting model using variations of data, Fuzzy Opt Decis Making, 18, 151-173 (2019) · Zbl 1437.62354 |
| [64] | Wang, W.; Liu, X., Fuzzy forecasting based on automatic clustering and axiomatic fuzzy set classification, Inf Sci, 294, 78-94 (2015) · Zbl 1360.62360 |
| [65] | Wasserman, L., All of nonparametric statistics (2007), New York: Springer, New York · Zbl 1099.62029 |
| [66] | Wei, LY, A GA-weighted ANFIS model based on multiple stock market volatility causality for TAIEX forecasting, Appl Soft Comput, 13, 911-920 (2013) |
| [67] | Wei, LY, A hybrid ANFIS model based on empirical mode decomposition for stock time series forecasting, Appl Soft Comput, 42, 368-376 (2016) |
| [68] | Wei, LY; Cheng, CH; Wu, HH, A hybrid ANFIS based on n-period moving average model to forecast TAIEX stock, Appl Soft Comput, 19, 86-92 (2014) |
| [69] | Woodward WA, Gray HL, Elliott AC, Boca Raton FL, (2011) Applied time series analysis. CRC Press · Zbl 1278.62009 |
| [70] | Ye, F.; Zhang, L.; Zhang, D.; Fujita, H.; Gong, Z., A novel forecasting method based on multi-order fuzzy time series and technical analysis, Inf Sci, 367-368, 41-57 (2016) · Zbl 1429.91310 |
| [71] | Yolcu, OC; Lam, HK, A combined robust fuzzy time series method for prediction of time series, Neurocomputing, 247, 87-101 (2017) |
| [72] | Yolcu, OC; Alpaslan, F., Prediction of TAIEX based on hybrid fuzzy time series model with single optimization process, Appl Soft Comput, 66, 18-33 (2018) |
| [73] | Yolcu, U.; Egrioglu, E.; Uslu, VR; Basaran, MA; Aladag, CH, A new approach for determining the length of intervals for fuzzy time series, Appl Soft Comput, 9, 647-651 (2009) · Zbl 05984567 |
| [74] | Yolcu, OC; Yolcu, U.; Egrioglu, E.; Aladag, CH, High order fuzzy timeseries forecasting method based on an intersection operation, Appl Math Model, 40, 8750-8765 (2016) · Zbl 1471.62480 |
| [75] | Zarei R, Akbari MG, Chachi J (2019) Modeling autoregressive fuzzy time series data based on semi-parametric methods. Soft Comput (In press) |
| [76] | Zhang, Y.; Qu, H.; Wang, W.; Zhao, J., A novel fuzzy time series forecasting model based on multiple linear regression and time series clustering, Math Probl Eng, 2020, 1-17 (2020) · doi:10.1155/2020/9546792 |
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