A Machine Learning Approach to Define Weights for Linear Combination of Forecasts

  • Ricardo Prudêncio
  • Teresa Ludermir
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4131)


The linear combination of forecasts is a procedure that has improved the forecasting accuracy for different time series. In this procedure, each method being combined is associated to a numerical weight that indicates the contribution of the method in the combined forecast. We present the use of machine learning techniques to define the weights for the linear combination of forecasts. In this paper, a machine learning technique uses features of the series at hand to define the adequate weights for a pre-defined number of forecasting methods. In order to evaluate this solution, we implemented a prototype that uses a MLP network to combine two widespread methods. The experiments performed revealed significantly accurate forecasts.


Forecast Error Forecast Method Machine Learn Approach Forecast Period Time Series Forecast 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Hibon, M., Evgeniou, T.: To combine or not to combine: selecting among forecasts and their combinations. International Journal of Forecasting 21(1), 15–24 (2004)Google Scholar
  2. 2.
    Adya, M., Armstrong, J.S., Collopy, F., Kennedy, M.: Automatic identification of time series features for rule-based forecasting. International Journal of Forecasting 17(2), 143–157 (2001)CrossRefGoogle Scholar
  3. 3.
    Arinze, B.: Selecting appropriate forecasting models using rule induction. Omega-International Journal of Management Science 22(6), 647–658 (1994)CrossRefGoogle Scholar
  4. 4.
    Rumelhart, D.E., Hinton, G.E., Williams, R.J.: Learning representations by backpropagation errors. Nature 323, 533–536 (1986)CrossRefGoogle Scholar
  5. 5.
    Harvey, A.: Time Series Models. MIT Press, Cambridge (1993)MATHGoogle Scholar
  6. 6.
    DeMenezes, L., Bunn, D., Taylor, J.: Review of guidelines for the use of combined forecasts. European Jour. of Operational Research 120, 190–204 (2000)CrossRefGoogle Scholar
  7. 7.
    Armstrong, J.: Findings from evidence-based forecasting: methods for reducing forecast error (2005), Available at: http://www.jscottarmstrong.com/ (Accessed on March 20 (2006)
  8. 8.
    Granger, C.W.J., Ramanathan, R.: Improved methods of combining forecasts. Journal of Forecasting 3, 197–204 (1984)CrossRefGoogle Scholar
  9. 9.
    Asku, C., Gunter, S.I.: An empirical analysis of the accuracy of SA, OLS, ERLS and NRLS combination of forecasts. Intern. Journal of Forecasting 8, 27–43 (1992)CrossRefGoogle Scholar
  10. 10.
    Makridakis, S., Hibon, M.: The M3-competition: results, conclusions and implications. International Journal of Forecasting 16(4), 451–476 (2000)CrossRefGoogle Scholar
  11. 11.
    Prudêncio, R., Ludermir, T.B.: Using Machine Learning Techniques to Combine Forecasting Methods. In: Webb, G.I., Yu, X. (eds.) AI 2004. LNCS (LNAI), vol. 3339, pp. 1122–1127. Springer, Heidelberg (2004)Google Scholar
  12. 12.
    Prechelt, L.: Proben 1: a set of neural network benchmark problems and benchmarking rules, Tech. Rep. 21/94, Fakultat fur Informatik, Karlsruhe (1994)Google Scholar
  13. 13.
    Demuth, H., Beale, M.: Neural Network Toolbox for Use with Matlab, The Mathworks Inc. (2003)Google Scholar
  14. 14.
    The Mathworks, Optimization Toolbox User’s Guide, The Mathworks Inc. (2003)Google Scholar
  15. 15.
    Flores, B.E.: Use of the sign test to supplement the percentage better statistic. International Journal of Forecasting 2, 477–489 (1986)CrossRefGoogle Scholar
  16. 16.
    Chu, C.-H., Widjaja, D.: Neural network system for forecasting method selection. Decision Support Systems 12(1), 13–24 (1994)CrossRefGoogle Scholar
  17. 17.
    Venkatachalan, A.R., Sohl, J.E.: An intelligent model selection and forecasting system. Journal of Forecasting 18, 167–180 (1999)CrossRefGoogle Scholar
  18. 18.
    Prudêncio, R., Ludermir, T.B.: Meta-learning approaches for selecting time series models. Neurocomputing Journal 61(C), 121–137 (2004)CrossRefGoogle Scholar
  19. 19.
    Prudêncio, R., Ludermir, T.B., DeCarvalho, F.: A modal symbolic classifier for selecting time series models. Pattern Recogn. Letters 25(8), 911–921 (2004)CrossRefGoogle Scholar
  20. 20.
    Giraud-Carrier, C., Vilalta, R., Brazdil, P.: Introduction to the special issue on meta-Learning. Machine Learning 54, 187–193 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ricardo Prudêncio
    • 1
  • Teresa Ludermir
    • 2
  1. 1.Departament of Information ScienceFederal University of PernambucoRecifeBrazil
  2. 2.Center of InformaticsFederal University of PernambucoRecifeBrazil

Personalised recommendations