Residual analysis and combination of embedding theorem and artificial intelligence in chaotic time series forecasting

Applied Artificial Intelligence

Volumn 25, Issue 1, 2011, Pages 45-73

  Ardalani Farsa, Muhammad ^a   Zolfaghari, Saeed ^a  

^a RYERSON UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; FORECASTING; GENETIC ALGORITHMS; PHASE SPACE METHODS; TIME SERIES ANALYSIS;

CHAOTIC BEHAVIOUR; CHAOTIC TIME SERIES; EMBEDDING THEOREMS; NEURAL-NETWORKS; PHASE-SPACE POINTS; RESIDUAL TIME; RESIDUALS ANALYSIS; TIME SERIES FORECASTING;

TIME SERIES;

EID: 79251498026     PISSN: 08839514     EISSN: 10876545     Source Type: Journal    
DOI: 10.1080/08839514.2011.529263     Document Type: Article

References (44)

1. Abarbanel, H. 1996. Analysis of observed chaotic data. New York: Spinger-Verlag.
2. Addison, P. S. 1997. Fractals and chaos: An illustrated course. Bristol and Philadelphia: Institute of Physics Publishing.
3. Aref, H. 1994. Stirring by chaotic advection. Journal of Fluid Mechanic 143:10-24.
4. Aubry, N., P. J. Holmes, J. L. Lumley, and E. Stone. 1988. The dynamics of coherent structures in the wall region of a turbulent boundary layer. Journal of Fluid Mechanics 192:115-173.
5. Cao, L. 1997. Practical method for determining the minimum embedding dimension of a scalar time series. Physica D 110:43-50.
6. Cho, K. B., and B. H. Wang. 1995. Radial basis function based adaptive fuzzy systems their applications to system identification and prediction. Fuzzy Sets and Systems 83:325-339.
7. Connor, J., and L. Atlas. 1993. Recurrent neural networks and time series prediction. Proceedings of the 15th Annual International Conference on Neural Networks, (IJC NN'91-Seattle). Seattle, WA, July 1991, 301-306.
8. Darwin, C. R. 1859. On the origin of species by means of natural selection. London: J. Murray.
9. Das, A., and P. Das. 2007. Chaotic analysis of the foreign exchange rates. Applied Mathematics and Computation 185:388-396.
10. Erramilli, A., and L. J. Forys. 1991. Oscillations and chaos in a flow model of a switching system. IEEE Journal on Selected Areas in Communications 9(2):171-178.
11. Harris, C. M., R. W. Todd, S. J. Bungard, R. W. Lovitt, J. G. Morris, and D. B. Kell. 1987. The dielectric permittivity of microbial suspensions at radio-frequencies: A novel method for the estimation of microbial biomass. Enzyme Microbial Technology 9:181-186.
12. Hibbert, B., and I. F. Wilkinson. 1994. Chaos theory and the dynamics of marketing systems. Journal of the Academy of Marketing Science 22(3):218-233.
13. Hilborn, R. C. 2001. Chaos and nonlinear dynamics: An introduction for scientists and engineers, Edition 2. Oxford: Oxford University Press.
14. Holland, J. H. 1975. Adaptation in natural and artificial systems. Ann Arbor, MI: University of Michigan Press.
15. Iokibe, T., Y. Fujimoto, M. Kanke, and S. Suzuki. 1997. Short-term prediction of chaotic time series by local fuzzy reconstruction method. Journal of Intelligent & Fuzzy Systems 5(1):3-21.
16. Jang, J. S. R., C. T. Sun, and E. Mizutani. 1997. Neuro-fuzzy and soft computing. Englewood Cliffs, NJ: Prentice-Hall.
17. Kaplan, D., and L. Glass. 1995. Understanding nonlinear dynamics. New York: Springer-Verlag.
18. Kennel, M. B. 1992. Method to distinguish possible chaos from colored noise and to determine embedding parameters. Physical Review A 46:3111-3118.
19. Kim, D., and C. Kim. 1997. Forecasting time series with genetic-fuzzy predictor ensemble. IEEE Transaction on Fuzzy Systems 5(4):523-535.
20. Kodogiannis, V., and A. Lolis. 2002. Forecasting financial time series using neural network and fuzzy system-based techniques. Neural Computing & Applications 11:90-102.
21. Lorenz, E. N. 1993. The essence of chaos. Seattle, WA: University of Washington Press.
22. Luk, K. C., J. E. Ball, and A. Sharma. 2000. A study of optimal model lag and spatial inputs to artificial neural networks for rainfall forecasting. Journal of Hydrology 227:56-65.
23. MacKay, R. S. 1993. Some thoughts on chaos in engineering. Presented at the 7th Toyota Conference: Toward the Harnessing of Chaos, 31 October-3 November 1993, Shizuoka, Japan.
24. MATLAB Release. 2009. The Math Works, Inc.
25. McNames, J. 1998. A nearest trajectory strategy for time series prediction. Proceedings of the International Workshop on Advanced Black-Box Techniques for Nonlinear Modeling, 112-128. Leuven, Belgium: Katholieke Universite it.
26. Nair, A. S., J. C. Liu, L. Rilett, and S. Gupta. 2001. Non-linear analysis of traffic flow. Proceedings of the 2001 IEEE Intelligent Transportation Systems, August 25-29. Oakland, CA, 681-685.
27. Qian, B., and K. Rasheed. 2007. Stock market prediction with multiple classifiers. Applied Intelligence 26:25-33.
28. Rojas, I., H. Pomares, J. L. Bernier, J. Ortega, B. Pino, F. J. Pelayo, and A. Prieto. 2002. Time series analysis using normalized PG-RBF network with regression weights. Neurocomputing 42:267-285.
29. Rojas, I., O. Valenzuelab, F. Rojasa, A. Guillena, L. J. Herreraa, H. Pomaresa, L. Marquezb, and M. Pasadasb. 2008. Soft-computing techniques and ARMA model for time series prediction. Neurocomputing 71:519-537.
30. Scott, S. 1991. Chemical chaos. Oxford: Oxford University Press.
31. Seiji, K., S. Hiroaki, and S. Hiroshi. 2004. Development of very-short-term load forecasting based on chaos theory. Electrical Engineering in Japan 148:55-63.
32. Sprott, J. C. 2003. Chaos and time series analysis (p. 105). Oxford: Oxford University Press.
33. Takens, F. 1981. Detecting strange attractors in turbulence. In Dynamic systems and turbulence, ed. D. A. Rand and L. S. Young, 366-381. Lecture Notes in Mathematics. Berlin: Springer Verlag.
34. Tenti, P. 1996. Forecasting foreign exchange rates using recurrent neural networks. Applied Artificial Intelligence 10:567-581.
35. Uzunoglu, V., and M. H. White. 1985. The synchronous oscillator: A synchronization and tracking network. IEEE Journal of Solid State Circuits 620:1214-1225.
36. Wang, L. X., and J. M. Mendel. 1992. Generating fuzzy rules by learning from examples. IEEE Transaction on Systems, Man, and Cybernetics 22(6):1414-1427.
37. Weiss, G. 1992. Chaos hits Wall Street-the theory that is. Business Week, p. 2.
38. Wichard, J. D., and M. Ogorzalek. 2004. Time series prediction with ensemble models. Presented at the Proceedings of the IJCNN 2004. July 25-29. Budapest, Hungary, 1625-1629.
39. Wilding, R. 1998a. Chaos theory: Implications for supply chain management. International Journal of Logistics Management 9:43-56.
40. Wilding, R. 1998b. Chaos, complexity and supply-chains. Logistics Focus - The Journal of the Institute of Logistics 6(8):8-10.
41. Wolf, A., J. B. Swift, H. L. Swinney, and J. A. Vastano. 1985. Determining Lyapunov exponents from a time series. Physica D 16:285-317.
42. Zhang, J., and K. F. Man. 1998. Time series prediction using recurrent neural network in multi-dimension embedding phase space. IEEE International Conference on Systems, Man, and Cybernetics 2:11-14.
43. Zhang, J., K. F. Man, and J. Y. Ke. 1998. Time series prediction using Lyapunov exponents in embedding phase space. Proceedings of the Fourth International Conference on Signal Processing 1:221-224.
44. Zhang, L. 1993. Artificial neural network model and its application. Shanghai: Fudan University Press.