Weighted Cross-Validation Evolving Artificial Neural Networks to Forecast Time Series

  • Juan Peralta Donate
  • Paulo Cortez
  • German Gutierrez Sanchez
  • Araceli Sanchis de Miguel
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 87)


Accurate time series forecasting is a key tool to support decision making and for planning our day to-day activities. In recent years, several works in the literature have adopted evolving artificial neural networks (EANN) for forecasting applications. EANNs are particularly appealing due to their ability to model an unspecified non-linear relationship between time series variables. In this work, a novel approach for EANN forecasting systems is proposed, where a weighted cross-validation is used to build an ensemble of neural networks. Several experiments were held, using a set of six real-world time series (from different domains) and comparing both the weighted and standard cross-validation variants. Overall, the weighted cross-validation provided the best forecasting results.


Evolutionary Computation Genetic Algorithms Artificial Neural Networks Time Series Forecasting Ensembles 


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  1. 1.
    Makridakis, S., Wheelwright, S., Hyndman, R.: Forecasting methods and applications. John Wiley & Sons, USA (2008)Google Scholar
  2. 2.
    Nunn, I., White, T.: The application of antigenic search techniques to time series forecasting. In: Proceedings of GECCO, pp. 353–360. ACM, New York (2005)Google Scholar
  3. 3.
    Zhang, G., Patuwo, B.E., Hu, M.Y.: Forecasting with artificial neural networks: The state of the art. International Journal of Forecasting 14, 35–62 (1998)CrossRefGoogle Scholar
  4. 4.
    Cortez, P., Rocha, M., Neves, J.: Time Series Forecasting by Evolutionary Neural Networks. In: Rubuñal, J., Dorado, J. (eds.) Artificial Neural Networks in Real-Life Applications, ch. III, pp. 47–70. Idea Group Publishing, Hershey (2006)Google Scholar
  5. 5.
    Peralta, J., Li, X., Gutierrez, G., Sanchis, A.: Time series forecasting by evolving artificial neural networks using genetic algorithms and differential evolution. In: Proceedings of IJCNN, pp. 3999–4006. IEEE, Los Alamitos (2010)Google Scholar
  6. 6.
    Kitano, H.: Designing Neural Networks using Genetic Algorithms with Graph Generation System. Complex Systems 4, 461–476 (1990)zbMATHGoogle Scholar
  7. 7.
    Yao, X.: Evolving Artificial Neural Networks. Proceedings of IEEE 9(87), 1423–1447 (2002)Google Scholar
  8. 8.
    Abraham, A.: Meta-Learning Evolutionary Artificial Neural Networks. Neurocomputing 56(c), 1–38 (2004)Google Scholar
  9. 9.
    Rocha, M., Cortez, P., Neves, J.: Evolution of Neural Networks for Classification and Regression. Neurocomputing 70(16-18), 2809–2816 (2007)CrossRefGoogle Scholar
  10. 10.
    Chena, Y., Chang, F.: Evolutionary artificial neural networks for hydrological systems forecasting. Journal of Hydrology 367(1-2), 125–137 (2009)CrossRefGoogle Scholar
  11. 11.
    Fogel, D.: Evolutionary Computation: Toward a New Philosophy of Machine Intelligence. Wiley-IEEE Press (1998)Google Scholar
  12. 12.
    Mosteller, F.: A k-sample slippage test for an extreme population. Annals of Mathematical Statistics, 101–109 (2006)Google Scholar
  13. 13.
    Sarkka, S., Vehtari, A., Lampinen, J.: CATS benchmark time series prediction by kalman smoother with cross-validated noise density. Neurocomputing 70(13-15), 2331–2341 (2007)CrossRefGoogle Scholar
  14. 14.
    Wah, B., Qian, M.: Time-series predictions using constrained formulations for neural-network training and cross validation. In: Proc. of 16th Int. Conf. on Intelligent Information Processing, pp. 220–226. Kluwer Academic Press, Dordrecht (2000)Google Scholar
  15. 15.
    Geman, S., Bienenstock, E., Doursat, R.: Neural networks and the bias/variance dilemma. Neural Computing 4(1), 1–58 (1992)CrossRefGoogle Scholar
  16. 16.
    Krogh, A., Sollich, P.: Statistical mechanics of ensemble learning. Physical Review E 55(1), 811–825 (1997)CrossRefGoogle Scholar
  17. 17.
    Yao, X., Islam, M.: Evolving artificial neural network ensembles. IEEE Computational Intelligence Magazine 3(1), 31–42 (2008)CrossRefGoogle Scholar
  18. 18.
    Hyndman, R.: Time series data library, (accessed September 2010)
  19. 19.
    Hyndman, R., Koehler, A.: Another look at measures of forecast accuracy. International Journal of Forecasting 22(4), 679–688 (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Juan Peralta Donate
    • 1
  • Paulo Cortez
    • 2
  • German Gutierrez Sanchez
    • 1
  • Araceli Sanchis de Miguel
    • 1
  1. 1.Computer Science DepartmentUniversity Carlos III of MadridLeganesSpain
  2. 2.Department of Information Systems/AlgoritmiUniversity of MinhoGuimarãesPortugal

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