Neural Computing and Applications

, Volume 16, Issue 4–5, pp 383–393 | Cite as

Extracting the main patterns of natural time series for long-term neurofuzzy prediction

  • Ali Gholipour
  • Caro Lucas
  • Babak N. Araabi
  • Masoud Mirmomeni
  • Masoud Shafiee
Original Article


A combination of singular spectrum analysis and locally linear neurofuzzy modeling technique is proposed to make accurate long-term prediction of natural phenomena. The principal components (PCs) obtained from spectral analysis have narrow band frequency spectra and definite linear or nonlinear trends and periodic patterns; hence they are predictable in large prediction horizon. The incremental learning algorithm initiates a model for each of the components as an optimal linear least squares estimation, and adds the nonlinear neurons if they help to reduce error indices over training and validation sets. Therefore, the algorithm automatically constructs the best linear or nonlinear model for each of the PCs to achieve maximum generalization, and the long-term prediction of the original time series is obtained by recombining the predicted components. The proposed method has been primarily tested in long-term prediction of some well-known nonlinear time series obtained from Mackey–Glass, Lorenz, and Ikeda map chaotic systems, and the results have been compared to the predictions made by multi-layered perceptron (MLP) and radial basis functions (RBF) networks. As a real world case study, the method has been applied to the long-term prediction of solar activity where the results have been compared to the long-term predictions of physical precursor and solar dynamo methods.


Long-term prediction Forecasting Singular spectrum analysis Locally linear neurofuzzy model Solar activity Sunspot number time series 


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Copyright information

© Springer-Verlag London Limited 2006

Authors and Affiliations

  • Ali Gholipour
    • 1
    • 2
  • Caro Lucas
    • 1
    • 2
  • Babak N. Araabi
    • 1
    • 2
  • Masoud Mirmomeni
    • 1
    • 2
  • Masoud Shafiee
    • 3
  1. 1.Control and Intelligent Processing Center of Excellence, Electrical and Computer Engineering DepartmentUniversity of TehranTehranIran
  2. 2.School of Cognitive SciencesInstitute for Studies in Theoretical Physics and MathematicsTehranIran
  3. 3.Faculty of Electrical EngineeringAmir Kabir University of TechnologyTehranIran

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