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Computación y Sistemas

Print version ISSN 1405-5546

Comp. y Sist. vol.10 n.1 México Jul./Sep. 2006


Statistical Characterization and Optimization of Artificial Neural Networks in Time Series Forecasting: The One–Period Forecast Case


Caracterización Estadística y Optimización de Redes Neuronales Artificiales para Pronóstico de Series de Tiempo: Pronóstico de un Solo Período


María Angélica Salazar Aguilar1, Guillermo J. Moreno Rodríguez2 and Mauricio Cabrera–Ríos*


1 División de Posgrado en Ingeniería de Sistemas, Facultad de Ingeniería Mecánica y Eléctrica, Universidad Autónoma de Nuevo León, Monterrey, Nuevo León, México e–mail

2 Ingeniería de Tráfico y Optimización de Capacidad, Avantel, Monterrey, Nuevo León, México e–mail


* Corresponding Author
Ph: +52(81) 1492 0637


Article received on Augost 09, 2005
Accepted on September 08, 2006



Time series forecasting is an active area for the application of Artificial Neural Networks (ANNs). Although the selection of an ANN has been greatly simplified, it remains a challenge to adequately determine the ANN's parameters. In this work a method based on statistical analysis and optimization techniques is proposed to select the ANN's parameters for application in time series forecasting. The results on the successful application of the method in a real demand forecasting problem for the telecommunications industry are also reported.

Keywords: Artificial Neural Networks, Time Series Forecasting, Design and Analysis of Experiments.



Los pronósticos de series de tiempo constituyen un área activa para la aplicación de Redes Neuronales Artificiales (RNAs). Aunque la selección de una RNA para tal aplicación se ha simplificado grandemente, la falta de un método establecido para asignar los parámetros de las RNAs de una manera adecuada sigue siendo un reto. En este trabajo se propone una metodología basada en técnicas estadísticas y optimización para la selección de parámetros de una RNA para el pronóstico de series de tiempo. La metodología propuesta se demuestra por medio de su aplicación en un problema real de pronóstico de demanda en la industria de las telecomunicaciones.

Palabras Clave: Redes Neuronales Artificiales, Series de tiempo, Análisis y Diseño de Experimentos, Pronósticos.





The authors are grateful to the CONACYT for the scholarship granted to Ms. Salazar for her graduate studies.



1. Bishop C. M., Neural Networks for Pattern Recognition, Oxford University Press, Oxford, UK, 1995.        [ Links ]

2. Box G. E. P., and Jenkins G. M., Time Series Analysis: Forecasting and Control, San Francisco, CA: Holden–Day, EUA, 1976.        [ Links ]

3. Cabrera–Ríos M., Castro J. M., and Mount–Campbell C. A., "Multiple quality criteria optimization in reactive in–mold coating with a data envelopment analysis approach II: a case with more than three performance measures", Journal of Polymer Engineering, Vol. 24, No. 4 , 2004, 435–450.        [ Links ]

4. Cabrera–Ríos M., Castro J. M., and Mount–Campbell C. A., "Multiple quality criteria optimization in in–mold coating (IMC) with a data envelopment analysis approach", Journal of Polymer Engineering, Vol. 22, No. 5, 2002, 305– 340.        [ Links ]

5. Castro C. E., Cabrera–Ríos M., Lilly B., Castro J. M., and Mount–Campbell C. A., "Identifying the best compromise between multiple performance measures in injection holding (IM) using data envelopment analysis (DEA)", Journal of Integrated Design and Process Science, Vol. 7, No. 1, 2003, 77–87.        [ Links ]

6. Castro J. M., Cabrera–Ríos M., and Mount–Campbell C. A., "Modelling and Simulation in reactive polymer processing", Modelling and Simulation in Materials Science and Engineering, Vol. 12, No. 3, 2004, S121–S149.        [ Links ]

7. Deb K., Multi–Objective Optimization Using Evolutionary Algorithms, Editorial Wiley, NY, EUA, 2004.        [ Links ]

8. Devore J. L., Probability and Statistics for Engineering the Sciences, 4ta Edition, Duxbury Press, California Polytechnic State University, EUA, 1995.        [ Links ]

9. Gardner M. W., and Dorling S. R., "Artificial neural networks (the multi–layer perceptron) – a review of applications in the atmospheric sciences", Atmospheric Environment, Vol. 33, 1999, 709–719.        [ Links ]

10. Hagan M. T., Demuth H. B., and Beale M., Neural Network Design, PWS Publishing Company, EUA, 1996.        [ Links ]

11. Hansen J. V., and Nelson R. D., "Forecasting and recombining time–series components by using neural networks", Journal of the Operations Research Society, No. 54, 2003, 307–317.        [ Links ]

12. Hillermeier C., Nonlinear Multiobjective Optimization: A Generalized Homotopy Approach, Basel: Birkhauser Verlag, 2001.        [ Links ]

13. Hornik K., Stinchcombe M., and White H., "Multilayer feedforward networks are universal approximators", Neural Networks, Vol. 2, No. 5, 1989, 359–366.        [ Links ]

14. Hu M. J. C., "Application in the Adaline system to weather forecasting", Master Thesis, Technical Report 6775–1, Stanford electronic Laboratories, Stanford, CA, June 1964.        [ Links ]

15. Hwarng H. B., "Insights into neural–network forecasting of time series corresponding to ARMA (p,q) structures", Omega: The International Journal of Management Science, Vol. 29, No. 3, 2001, 273–289.        [ Links ]

16. Kolarik T., and G. Rudorfer, "Time series forecasting using neural networks", Conference Proceedings of the International Conference on APL 1994. APL Quote Quad, Vol. 25, No. 1, 1994, 86–94.        [ Links ]

17. Kolehmainen M., Martikainen H., Russkanen J., "Neural networks and periodic components used in air quality forecasting", Atmospheric Environment, Vol. 35, 2001, 815–825.        [ Links ]

18. Liao K–P., and Fildes R., "The accuracy of a procedural approach to specifying feedforward neural networks for forecasting", Computers & Operations Research, Vol. 32, No. 2, 2005, 151–2169.        [ Links ]

19. Maier H. R., and Dandy G. C., "Neural networks for the prediction and forecasting of water resources variables: a review of modelling issues and applications", Environment Modelling & Software, Vol. 15, 2000, 101–124.        [ Links ]

20. Makridakis S., Anderson A., Carbone R., Fildes R., Hibbon M., Lewandowski R., Newton J., Parsen E., and Winkley R., "The accuracy of extrapolation (time series) methods: Results of a forecasting competition", Journal of Forecasting, Vol. 1, 1982, 111–153.        [ Links ]

21. Makridakis S., and Wheelwright S. C., The Handbook of Forecasting a Manager's Guide, 2da Edition, Editorial Wiley, NY, EUA, 1987.        [ Links ]

22. Medeiros M. C., and Pedreira C. E., "What are the effects of forecasting linear time series with neural networks?" Logistic and Transportation Review, Vol. 31, No. 3, 2001, 239–251.        [ Links ]

23. Niska Harri, Hiltunen Teri, Karppinen Ari, Russkanen J. and Kolehmainen M., "Evolving the neural network model for forecasting air pollution time series", Engineering Applications of Artificial Intelligence, Vol. 17, 2004, 159–167.        [ Links ]

24. Piramuthu S., H. Ragavan, and M. Shaw, "Using feature construction to improve the performance of neural networks", Management Science, Vol. 44, No. 3, 1998, 416–430.        [ Links ]

25. R. J. Kuo and K. C. Xue, "Fuzzy neural networks with application to sales forecasting", Fuzzy sets and y systems, Vol. 108, No. 2, 1999, 123–143.        [ Links ]

26. Rumelhart D–E., Hinton G. E., and Willians R. J., "Learning representations by backpropagating errors", Nature, 323 (6188), 1986, 533–536.        [ Links ]

27. Sexton R. S., McMurtrey S., Michalopoulos J. O., and Smith A. M., "Employee turnover: a neural network solution", Computers & Operations Research, Vol. 32, No. 10, 2005, 2635–2651.        [ Links ]

28. Smith K. A. and Gupta JND, "Neural networks in business: techniques and applications for the operations researcher", Computers and Operations Research, Vol. 27, Num. 11–12, 2000, 1023–1044.        [ Links ]

29. Werbos P. J., "Generalization of backpropagation with applications to a recurrent gas market model", Neural Networks, Vol. 1, 1988, 339–356.        [ Links ]

30. White H., "Connectionist nonparametric regression: Multilayer feedforward networks can learn arbitrary mappings", Neural Networks, Vol. 3, No. 5, 1990, 535–549.        [ Links ]

31. Widrow B., Rumelhart D., and Lehr M. A., "Neural networks: Applications in industry, business and science", Communications of the ACM, Vol. 37, No. 3, 1994, 93–105.        [ Links ]

32. Zhang G., Patuwo E., and Hu Y. M., "Forecasting with artificial neural networks the state of the art", International Journal of Forecasting, Vol.14, No. 1, 1998, 35–62.        [ Links ]

33. Zhang G. P., Neural Networks in Business Forecasting, Idea Group Publishing, Georgia State University, EUA, 2004.        [ Links ]

34. Zhang G. P., and Hu M. Y., "A simulation study of artificial neural networks for nonlinear time series forecasting", Computers & Operations Research, Vol. 28, 2001, 381–396.        [ Links ]

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