Intelligent financial time series forecasting: A complex neuro-fuzzy approach with multi-swarm intelligence

Li, C. ; Chiang, T. W.

International Journal of Applied Mathematics and Computer Science, Tome 22 (2012) no. 4, pp. 787-800.

Résumé

Financial investors often face an urgent need to predict the future. Accurate forecasting may allow investors to be aware of changes in financial markets in the future, so that they can reduce the risk of investment. In this paper, we present an intelligent computing paradigm, called the Complex Neuro-Fuzzy System (CNFS), applied to the problem of financial time series forecasting. The CNFS is an adaptive system, which is designed using Complex Fuzzy Sets (CFSs) whose membership functions are complex-valued and characterized within the unit disc of the complex plane. The application of CFSs to the CNFS can augment the adaptive capability of nonlinear functional mapping, which is valuable for nonlinear forecasting. Moreover, to optimize the CNFS for accurate forecasting, we devised a new hybrid learning method, called the HMSPSO-RLSE, which integrates in a hybrid way the so-called Hierarchical Multi-Swarm PSO (HMSPSO) and the well known Recursive Least Squares Estimator (RLSE). Three examples of financial time series are used to test the proposed approach, whose experimental results outperform those of other methods.

Détail

Keywords: complex fuzzy set, complex neuro fuzzy system, hierarchical multi swarm, particle swarm optimization (PSO), recursive least squares estimator, time series forecasting
Mots-clés : zbiór rozmyty, system neuronowo-rozmyty, optymalizacja rojem cząstek, szereg czasowy

Bibliographie

[1] Albus, J. S. (1975). Data storage in the cerebellar model articulation controller (CMAC), Journal of Dynamic Systems, Measurement and Control 97(2): 228-233.

[2] Boyacioglu, M. A. and Avci, D. (2010). An adaptive network-based fuzzy inference system (ANFIS) for the prediction of stock market return: The case of the Istanbul stock exchange, Expert Systems with Applications 37(12): 7908-7912.

[3] Brdyś, M. A., Borowa, A., Idźkowiak, P. and Brdyś, M. T. (2009). Adaptive prediction of stock exchange indices by state space wavelet networks, International Journal of Applied Mathematics and Computer Science 19(2): 337-348, DOI: 10.2478/v10006-009-0029-z.

[4] Buckley, J. J. (1989). Fuzzy complex numbers, Fuzzy Sets and Systems 33(3): 333-345.

[5] Castro, J. L. (1995). Fuzzy logic controllers are universal approximators, IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans 25(4): 629-635.

[6] Chen, Z., Aghakhani, S., Man, J. and Dick, S. (2011). ANCFIS: A neurofuzzy architecture employing complex fuzzy sets, IEEE Transactions on Fuzzy Systems 19(2): 305-322.

[7] Deng, X. and Wang, X. (2009). Incremental learning of dynamic fuzzy neural networks for accurate system modeling, Fuzzy Sets and Systems 160(7): 972-987.

[8] Dick, S. (2005). Toward complex fuzzy logic, IEEE Transactions on Fuzzy Systems 13(3): 405-414.

[9] Eberhart, R. and Kennedy, J. (1995). A new optimizer using particle swarm theory, Proceedings of the 6th International Symposium on Micro Machine and Human Science, MHS 1995, Nagoya, Japan, pp. 39-43.

[10] Gao, Y. and Er, M. J. (2005). Narmax time series model prediction: Feedforward and recurrent fuzzy neural network approaches, Fuzzy Sets and Systems 150(2): 331-350.

[11] Graves, D. and Pedrycz, W. (2009). Fuzzy prediction architecture using recurrent neural networks, Neurocomputing 72(7-9): 1668-1678.

[12] Hornik, K., Stinchcombe, M. and White, H. (1989). Multilayer feedforward networks are universal approximators, Neural Networks 2(5): 359-366.

[13] Jang, J. S. R. (1993). ANFIS: adaptive-network-based fuzzy inference system, IEEE Transactions on Systems, Man, and Cybernetics 23(3): 665-685.

[14] Kennedy, J. and Eberhart, R. (1995). Particle swarm optimization, IEEE International Conference on Neural Networks, Perth, Australia, pp. 1942-1948.

[15] Khashei, M. and Bijari, M. (2011). A novel hybridization of artificial neural networks and ARIMA models for time series forecasting, Applied Soft Computing 11(2): 2664-2675.

[16] Kim, J. and Kasabov, N. (1999). HYFIS: Adaptive neuro-fuzzy inference systems and their application to nonlinear dynamical systems, Neural Networks 12(9): 1301-1319.

[17] Li, C. and Cheng, H.-H. (2011). Intelligent forecasting of S 500 time series-A self-organizing fuzzy approach, in N. T. Nguyen, C.-G. Kim and A. Janiak (Eds.), Intelligent Information and Database Systems, Lecture Notes in Artificial Intelligence, Vol. 6592, Springer-Verlag, Berlin/Heidelberg, pp. 411-420.

[18] Li, C. and Chiang, T.-W. (2011a). Complex fuzzy computing to time series prediction-A multi-swarm PSO learning approach, in N. T. Nguyen, C.-G. Kim and A. Janiak (Eds.) Intelligent Information and Database Systems, Lecture Notes in Artificial Intelligence, Vol. 6592, Springer-Verlag, Berlin/Heidelberg, pp. 242-251.

[19] Li, C. and Chiang, T.-W. (2011b). Complex fuzzy model with PSO-RLSE hybrid learning approach to function approximation, International Journal of Intelligent Information and Database Systems 5(4): 409-430.

[20] Li, C. and Chiang, T.-W. (2011c). Function approximation with complex neuro-fuzzy system using complex fuzzy sets-A new approach, New Generation Computing 29(3): 261-276.

[21] Li, C., Chiang, T.-W., J.-W., H. and Wu, T. (2010). Complex neuro-fuzzy intelligent approach to function approximation, 3rd International Workshop on Advanced Computational Intelligence, IWACI 2010, Suzhou, China, pp. 151-156.

[22] Li, C. and Lee, C.-Y. (2003). Self-organizing neuro-fuzzy system for control of unknown plants, IEEE Transactions on Fuzzy Systems 11(1): 135-150.

[23] Li, C., Lee, C.-Y. and Cheng, K.-H. (2004). Pseudoerror-based self-organizing neuro-fuzzy system, IEEE Transactions on Fuzzy Systems 12(6): 812-819.

[24] Li, C. and Priemer, R. (1997). Self-learning general purpose PID controller, Journal of the Franklin Institute 334(2): 167-189.

[25] Li, C. and Priemer, R. (1999). Fuzzy control of unknown multiple-input-multiple-output plants, Fuzzy Sets and Systems 104(2): 245-267.

[26] Lu, C.-J., Lee, T.-S. and Chiu, C.-C. (2009). Financial time series forecasting using independent component analysis and support vector regression, Decision Support Systems 47(2): 115-125.

[27] Man, J. Y., Chen, Z. and Dick, S. (2007). Towards inductive learning of complex fuzzy inference systems, Annual Meeting of the North American Fuzzy Information Processing Society, NAFIPS 2007, San Diego, CA, USA, pp. 415-420.

[28] Mansour, M. M., Mekhamer, S. F. and El-Kharbawe, N.-S. (2007). A modified particle swarm optimizer for the coordination of directional overcurrent relays, IEEE Transactions on Power Delivery 22(3): 1400-1410.

[29] Moody, J. and Darken, C. J. (1989). Fast learning in networks of locally-tuned processing units, Neural Computation 1(2): 281-294.

[30] Moses, D., Degani, O., Teodorescu, H. N., Friedman, M. and Kandel, A. (1999). Linguistic coordinate transformations for complex fuzzy sets, IEEE International Fuzzy Systems Conference Proceedings, FUZZ-IEEE 1999, Seoul, Korea, pp. 1340-1345.

[31] Mousavi, S. J., Ponnambalam, K. and Karray, F. (2007). Inferring operating rules for reservoir operations using fuzzy regression and ANFIS, Fuzzy Sets and Systems 158(10): 1064-1082.

[32] Niu, B., Zhu, Y., He, X. and Wu, H. (2007). MCPSO: A multi-swarm cooperative particle swarm optimizer, Applied Mathematics and Computation 185(2): 1050-1062.

[33] Paul, S. and Kumar, S. (2002). Subsethood-product fuzzy neural inference system (SUPFUNIS), IEEE Transactions on Neural Networks 13(3): 578-599.

[34] Ramot, D., Friedman, M., Langholz, G. and Kandel, A. (2003). Complex fuzzy logic, IEEE Transactions on Fuzzy Systems 11(4): 450-461.

[35] Ramot, D., Milo, R., Friedman, M. and Kandel, A. (2002). Complex fuzzy sets, IEEE Transactions on Fuzzy Systems 10(2): 171-186.

[36] Rojas, I., Valenzuela, O., Rojas, F., Guillen, A., Herrera, L. J., Pomares, H., Marquez, L. and Pasadas, M. (2008). Soft-computing techniques and ARMA model for time series prediction, Neurocomputing 71(4-6): 519-537.

[37] Simiński, K. (2010). Rule weights in a neuro-fuzzy system with a hierarchical domain partition, International Journal of Applied Mathematics and Computer Science 20(2): 337-347, DOI: 10.2478/v10006-010-0025-3.

[38] Smetek, M. and Trawinski, B. (2011). Selection of heterogeneous fuzzy model ensembles using self-adaptive genetic algorithms, New Generation Computing 29(3): 309-327.

[39] Tung, W. L. and Quek, C. (2011). Financial volatility trading using a self-organising neural-fuzzy semantic network and option straddle-based approach, Expert Systems with Applications 38(5): 4668-4688.

[40] Vo, N., Quang, T., Dinh, T. and Dinh, T. (2011). Robust visual tracking using randomized forest and online appearance model, in N. T. Nguyen, C.-G. Kim and A. Janiak (Eds.), Intelligent Information and Database Systems, Lecture Notes in Artificial Intelligence, Vol. 6592, Springer-Verlag, Berlin/Heidelberg pp. 212-221.

[41] Yahoo Finance for Hang Seng Index (2011). Website: http://finance.yahoo.com/q?s=ˆHSI.

[42] Yahoo Finance for Nikkei 225 Index (2011). Website, http://finance.yahoo.com/q?s=ˆN225.

[43] Yahoo Finance for Taiwan Stock Exchange Capitalization Weighted Stock Index (2011). Website, http://finance.yahoo.com/q?s=ˆTWII.

[44] Yuhui, S. and Eberhart, R. C. (2001). Fuzzy adaptive particle swarm optimization, Proceedings of the 2001 Congress on Evolutionary Computation, Seoul, Korea, pp. 101-106.

[45] Zhang, G., Dillon, T. S., Cai, K.-Y., Ma, J. and Lu, J. (2009). Operation properties and \delta-equalities of complex fuzzy sets, International Journal of Approximate Reasoning 50(8): 1227-1249.