Robust Estimator for the Learning Process in Neural Networks Applied in Time Series

  • Héctor Allende
  • Claudio Moraga
  • Rodrigo Salas
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2415)

Abstract

Artificial Neural Networks (ANN) have been used to model non-linear time series as an alternative of the ARIMA models. In this paper Feedforward Neural Networks (FANN) are used as non-linear autoregressive (NAR) models. NAR models are shown to lack robustness to innovative and additive outliers. A single outlier can ruin an entire neural network fit. Neural networks are shown to model well in regions far from outliers, this is in contrast to linear models where the entire fit is ruined. We propose a robust algorithm for NAR models that is robust to innovative and additive outliers. This algorithm is based on the generalized maximum likelihood (GM) type estimators, which shows advantages over conventional least squares methods. This sensitivity to outliers is demostrated based on a synthetic data set.

Keywords

Feedforward ANN Nonlinear Time Series Robust Learning 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Allende H., Moraga C.: Time Series Forecasting with Neural Networks. Forschungsbericht N∘ 727/2000. Universitaet Dortmund Fachbereich Informatik. (2000)Google Scholar
  2. 2.
    Allende H., Heiler S.: Recursive Generalized M-Estimates for Autoregressive Moving Average Models. Journal of Time Series Analysis. 13 (1992) 1–18MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Box G.E., Jenkins G.M. and Reinsel G.C: Time Series Analysis, Forecasting and Control. Ed. Prentice Hall. (1994)Google Scholar
  4. 4.
    Chen C., Liu L.M.: Forecasting time series with outliers. J. Forecast. 12 (1993) 13–35CrossRefGoogle Scholar
  5. 5.
    Connor J. T., Martin R. D.: Recurrent Neural Networks and Robust Time Series Prediction. IEEE Transactions of Neural Networks 52 (1994) 240–253CrossRefGoogle Scholar
  6. 6.
    Connor J.T.: A robust Neural Networks Filter for Electricity Demand Prediction. J. of Forecasting 15 (1996) 437–458CrossRefGoogle Scholar
  7. 7.
    Gabr M.M.: Robust estimation of bilinear time series models. Comm. Statist. Theory and Meth 27 1 (1998) 41–53CrossRefMathSciNetGoogle Scholar
  8. 8.
    Fox A. J.: Outliers in time series. J. Royal Statist. Soc. Ser B 43 (1972) 350–363Google Scholar
  9. 9.
    Hampel F.R., Ronchetti E.M., Rousseeuw P.J., Stahel W.A. Robust Statistics. Wiley Series in Probability and Mathematical Statistics. (1986)Google Scholar
  10. 10.
    Schoen F.: Stochastic techniques for global optimization: a survey of recent advances, J. Global Optim. 1, 3 (1991) 207–228CrossRefMathSciNetGoogle Scholar
  11. 11.
    Weigend A., Gershenfeld N.: Time Series Prediction: Forecasting the Future and Understanding the Past: Proceedings of the NATO Advanced Research Workshop on Comparative Time Series. (1993)Google Scholar
  12. 12.
    White H.: Artificial Neural Networks: Approximation and Learning Theory, Basil Blackwell, Oxford (1992)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Héctor Allende
    • 1
    • 4
  • Claudio Moraga
    • 2
    • 3
  • Rodrigo Salas
    • 1
  1. 1.Dept. de InformáticaUniversidad Técnica Federico Santa MaríaCasillaChile
  2. 2.Dept. Artificial IntelligenceTechnical University of MadridBoadilla del Monte MadridSpain
  3. 3.Department of Computer ScienceUniversity of DortmundDortmundGermany
  4. 4.Facultad de Ciencia y TecnologíaUniversidad Adolfo IbañezGermany

Personalised recommendations