×

Long-term forecasting of time series based on linear fuzzy information granules and fuzzy inference system. (English) Zbl 1401.62181

Summary: Long-term time series forecasting is a challenging problem both in theory and in practice. Although the idea of information granulation has been shown to be an essential concept and algorithmic pursuit in time series prediction, there is still an acute need for developing a sound conceptual framework for time series prediction so that information granulation can capture the essence of collections of data better, including average and trend information. In this paper, a novel type of fuzzy information granule involving a time-dependent (non-stationary) membership function is proposed to structure numerical time series into granular time series. We show that the underlying arithmetic along with the concept of distance for this type of information granules can be expressed in a simple way, which facilitates the ensuing processing of information granules. With this regard, distances between observation granules and antecedent granules presented in fuzzy rules can be easily determined. The design of long-term prediction method based on fuzzy inference system is then realized through interpolation completed with the aid of fuzzy rules. Experiments involving chaotic Mackey-Glass time series and real-world time series demonstrate that the proposed model produces better long-term forecasting than some existing numeric models such as Autoregressive (AR) models, nonlinear autoregressive (NAR) neural networks, Support Vector Regression (SVR) and fuzzy inference systems involving triangular and interval information granules.

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
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ruan, J.; Wang, X.; Shi, Y., Developing fast predictors for large-scale time series using fuzzy granular support vector machines, Appl. Soft Comput., 13, 3981-4000 (2013)
[2] Box, G.; Jenkins, G., Time Series Analysis: Forecasting and Control (1976), Holden-Day: Holden-Day San Francisco
[3] Duran, M. J.; Cros, D.; Riquelme, J., Short-term wind power forecast based on ARX models, J. Energy Eng., 133, 3, 172-180 (2007)
[4] Pappas, S. S.; Ekonomou, L.; Karamousantas, D. C.; Chatzarakis, G.; Katsikas, S.; Liatsis, P., Electricity demand loads modeling using AutoRegressive Moving Average (ARMA) models, Energy, 33, 9, 1353-1360 (2008)
[5] Erdem, E.; Shi, J., ARMA based approaches for forecasting the tuple of wind speed and direction, Appl. Energy, 88, 4, 1405-1414 (2011)
[6] Box, G. E.P.; Jenkins, G. M.; Reinsel, G. C., Time Series Analysis: Forecasting and Control (2008), John Wiley & Sons: John Wiley & Sons New York · Zbl 1154.62062
[7] McLeod, A. I.; Li, W. K., Diagnostic checking ARMA time series models using squared-residual to correlations, J. Time Ser. Anal., 4, 4, 269-273 (1983) · Zbl 0536.62067
[8] Jilani, T. A.; Burney, S. M.A., M-factor high order fuzzy time series forecasting for road accident data: analysis and design of intelligent systems using soft computing techniques, Adv. Soft Comput., 41, 246-254 (2007)
[9] Bennett, Christopher; Stewart, Rodney A.; Beal, Cara D., ANN-based residential water end-use demand forecasting model, Expert Syst. Appl., 40, 1014-1023 (2013)
[10] Elsafi, Sulafa Hag, Artificial neural networks (ANNs) for flood forecasting at Dongola Station in the River Nile, Sudan, Alex. Eng. J., 53, 3, 655-662 (2014)
[11] Ahmad, A. S.; Hassan, M. Y.; Abdullah, M. P.; Rahman, H. A.; Hussin, F.; Abdullah, H.; Saidur, R., A review on applications of ANN and SVM for building electrical energy consumption forecasting, Renew. Sustain. Energy Rev., 33, 2, 102-109 (2014)
[12] Benmouiza, Khalil; Cheknane, Ali, Forecasting hourly global solar radiation using hybrid k-means and nonlinear autoregressive neural network models, Energy Convers. Manag., 75, 561-569 (2013)
[13] Tugřul Seyhan, A.; Tayfur, Gökmen; Karakurt, Murat; Tanogľu, Metin, Artificial neural network (ANN) prediction of compressive strength of VARTM processed polymer compositesOriginal, Comput. Mater. Sci., 34, 1, 99-105 (2005)
[14] Vapnik, V., The Nature of Statistical Learning Theory (1995), Springer Verlag: Springer Verlag New York · Zbl 0833.62008
[15] Lu, C. J.; Lee, T. S.; Chiu, C. C., Financial time series forecasting using independent component analysis and support vector regression, Decis. Support Syst., 47, 2, 115-125 (2009)
[16] Baydaroglu, Ö.; Koçak, K., SVR-based prediction of evaporation combined with chaotic approach, J. Hydrol., 508, 356-363 (2014)
[17] Wen, F.; Xiao, J.; He, Z.; Gong, X., Stock price prediction based on SSA and SVM, Proc. Comput. Sci., 31, 625-631 (2014)
[18] Tay, F. E.H.; Cao, L. J., Modified support vector machines in financial time series forecasting, Neurocomputing, 48, 1-4, 847-861 (2002) · Zbl 1006.68777
[19] Kaneda, Y.; Ibayashi, H.; Oishi, N.; Mineno, H., Greenhouse environmental control system based on SW-SVR, Proc. Comput. Sci., 60, 860-869 (2015)
[20] Danenas, P.; Garsva, G., Support vector machines and their application in credit risk evaluation process, Transf. Bus. Econ., 8, 46-58 (2009)
[21] Gunduz, Y.; Uhrig-Homburg, M., Predicting credit default swap prices with financial and pure data-driven approaches, Quant. Finance, 11, 1709-1727 (2011) · Zbl 1277.91185
[22] Chen, Z. Y.; Fan, Z. P.; Sun, M. H., A hierarchical multiple kernel support vector machine for customer churn prediction using longitudinal behavioral data, Eur. J. Oper. Res., 223, 461-472 (2012) · Zbl 1292.68131
[23] Wu, S. M.; Akbarov, A., Support vector regression for warranty claim forecasting, Eur. J. Oper. Res., 213, 196-204 (2011) · Zbl 1237.62179
[24] Lin, Tzu-Chao, A multi-class Dempster classifier with support vector machine for image enhancement, Int. J. Innov. Comput. Inf. Control, 11, 5, 1639-1653 (2015)
[25] Chen, R. C.; Cheng, K. F.; Hsieh, C. F., Using rough set and support vector machine for network intrusion detection system, Int. J. Netw. Secur. Appl., 1, 1, 1-13 (2009)
[26] Wu, C. H.; Tzeng, G. H.; Goo, Y. J.; Fang, W. C., A real-valued genetic algorithm to optimize the parameters of support vector machine for predicting bankruptcy, Expert Syst. Appl., 32, 397-408 (2007)
[27] Liu, Y.; Wang, R. X., Study on network traffic forecast model of SVR optimized by GAFSA, Chaos Solitons Fractals, 89, 153-159 (2016) · Zbl 1360.62470
[28] Nieto, P. J.G.; Garcia-Gonzalo, E.; Lasheras, F. S.; Juez, F. J.D., Hybrid PSO-SVM-based method for forecasting of the remaining useful life for aircraft engines and evaluation of its reliability, Reliab. Eng. Syst. Saf., 138, 219-231 (2015)
[29] Wang, X.; Xiao, X.; Xiao, Z., S-reits’ performance forecast using a small sample model associating support vector machine with vector auto-regression model, Int. J. Innov. Comput. Inf. Control, 12, 1, 15-40 (2016)
[30] Willis, H. I.; Northcote-Green, J. E.D., Comparison tests of fourteen distribution load forecasting methods, IEEE Trans. Power Appar. Syst., 103, 6, 1190-1197 (1984)
[31] Aneiros, G.; Vilar, J.; Raña, P., Short-term forecast of daily curves of electricity demand and price, Int. J. Electr. Power Energy Syst., 80, 96-108 (2016)
[32] Simon, G.; Lendasse, A.; Cottrell, M.; Fort, J.; Verleysen, M., Time series forecasting long term trends with self-organizing maps, Pattern Recognit. Lett., 26, 1795-1808 (2005)
[33] Wang, W.; Pedrycz, W.; Liu, X., Time series long-term forecasting model based on information granules and fuzzy clustering, Eng. Appl. Artif. Intell., 41, 17-24 (2015)
[34] Zadeh, L. A., Fuzzy sets and information granularity, Adv. Fuzzy Set Theory Appl., 1, 3-18 (1979)
[35] Pedrycz, W.; Vukovich, G., Abstraction and specialization of information granules, IEEE Trans. Syst. Man Cybern., Part B, Cybern., 31, 106-111 (2001)
[36] Wang, L.; Liu, X.; Pedrycz, W., Effective intervals determined by information granules to improve forecasting in fuzzy time series, Expert Syst. Appl., 40, 5673-5679 (2013)
[37] Wang, L.; Liu, X.; Pedrycz, W.; Shao, Y., Determination of temporal information granules to improve forecasting in fuzzy time series, Expert Syst. Appl., 41, 3134-3142 (2014)
[38] Lu, W.; Pedrycz, W.; Liu, X.; Yang, J.; Li, P., The modeling of time series based on fuzzy information granules, Expert Syst. Appl., 41, 3799-3808 (2014)
[39] Hryniewicz, O.; Kaczmarek, K., Bayesian analysis of time series using granular computing approach, Appl. Soft Comput., 47, 644-652 (2016)
[40] Lu, W.; Zhang, L.; Pedrycz, W.; Yang, J.; Liu, X., The granular extension of Sugeno-type fuzzy models based on optimal allocation of information granularity and its application to forecasting of time series, Appl. Soft Comput., 42, 38-52 (2016)
[41] Lu, W.; Chen, X.; Pedrycz, W.; Liu, X.; Yang, J., Using interval information granules to improve forecasting in fuzzy time series, Int. J. Approx. Reason., 57, 1-18 (2015) · Zbl 1337.62306
[42] Chen, M. Y.; Chen, B. T., A hybrid fuzzy time series model based on granular computing for stock price forecasting, Inf. Sci., 294, 227-241 (2015)
[43] Bargiela, A.; Pedrycz, W., Granulation of Temporal Data: A Global View on Time Series, 191-196 (2003)
[44] Dong, R.; Pedrycz, W., A granular time series approach to long-term forecasting and trend forecasting, Physica A, 387, 3253-3270 (2008)
[45] Yu, F.; Dong, K.; Chen, F.; Jiang, Y.; Zeng, W., Clustering time series with granular dynamic time warping method, (IEEE International Conference on Granular Computing (2007)), 393
[46] Bargiela, A.; Pedrycz, W., Granular Computing: An Introduction (2003), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 1046.68052
[47] Diamond, P.; Kloeden, P., Metric topology of fuzzy differential equations, IEEE Trans. Fuzzy Syst., 8, 583-590 (2000)
[48] Nguyen, H. T., A note on the extension principle for fuzzy sets, J. Math. Anal. Appl., 64, 369-380 (1978) · Zbl 0377.04004
[49] Barros, L. C.; Bassanezi, R. C.; Tonelli, P. A., On the continuity of the Zadeh’s extension, (Proc. IFSA 1997 Congress. Proc. IFSA 1997 Congress, Prague (1997))
[50] Bede, B., Mathematics of Fuzzy Sets and Fuzzy Logic (2013), Springer: Springer Heidelberg, New York, Dordrecht, London · Zbl 1271.03001
[51] Erceg, M. A., Metric spaces in fuzzy set theory, J. Math. Anal. Appl., 69, 205-230 (1979) · Zbl 0409.54007
[52] Chang, Y.; Chen, S.; Liau, C., Fuzzy interpolative reasoning for sparse fuzzy rule-based systems based on the areas of fuzzy sets, IEEE Trans. Fuzzy Syst., 16, 1285-1301 (2008)
[53] Yan, X.; Su, X., Linear Regression Analysis: Theory and Computing, 1-2 (2009), World Scientific Publishing CO. Pte. Ltd.: World Scientific Publishing CO. Pte. Ltd. Singapore
[54] This time series is from
[55] This time series is from
[56] This time series is from
[57] This time series is from
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.