Title: Synergy of chaos theory and artificial neural networks in chaotic time series forecasting

Authors: Muhammad Ardalani-Farsa, Saeed Zolfaghari

Addresses: Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Ontario M5B 2K3, Canada. ' Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Ontario M5B 2K3, Canada

Abstract: A unique technique based on chaos theory and artificial neural networks (ANN) is developed to analyse and forecast chaotic time series. An embedding theorem is used to determine the embedding parameters. Accordingly the chaotic time series is reconstructed into phase space points. Based on chaos theory, there exists an unknown mathematical equation which can forecast the future value of the phase space points. Therefore, the embedded phase space points are fed into a neural network and trained. When the unknown phase space is predicted, the future value of time series is obtained accordingly. Two neural network architectures, feedforward and Elman, are utilised in this study. The Mackey-Glass (M-G), logistic and Henon time series are used to validate the performance of the proposed technique. The numerical experimental results confirm that the proposed method can forecast the chaotic time series effectively and accurately when compared with the existing forecasting methods.

Keywords: chaotic time series; embedding theorem; artificial neural networks; ANNs; recurrent neural networks; RNNs; forecasting; chaos theory.

DOI: 10.1504/IJAMS.2011.040230

International Journal of Applied Management Science, 2011 Vol.3 No.2, pp.121 - 142

Published online: 30 Sep 2014 *

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