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

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  • Muhammad Ardalani-Farsa
  • Saeed Zolfaghari
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    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.

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    Bibliographic Info

    Article provided by Inderscience Enterprises Ltd in its journal Int. J. of Applied Management Science.

    Volume (Year): 3 (2011)
    Issue (Month): 2 ()
    Pages: 121-142

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    Handle: RePEc:ids:injams:v:3:y:2011:i:2:p:121-142

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    Web page: http://www.inderscience.com/browse/index.php?journalID=286

    Related research

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

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