A Hybrid Model for Symbolic Interval Time Series Forecasting

  • André Luis S. Maia
  • Francisco de A.T. de Carvalho
  • Teresa B. Ludermir
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4233)


This paper presents two approaches to symbolic interval time series forecasting. The first approach is based on the autoregressive moving average (ARMA) model and the second is based on a hybrid methodology that combines both ARMA and artificial neural network (ANN) models. In the proposed approaches, two models are respectively fitted to the mid-point and range of the interval values assumed by the symbolic interval time series in the learning set. The forecast of the lower and upper bounds of the interval value of the time series is accomplished through the combination of forecasts from the mid-point and range of the interval values. The evaluation of the proposed models is based on the estimation of the average behaviour of the mean absolute error and mean square error in the framework of a Monte Carlo experiment.


Time Series Hybrid Model ARMA Model Time Series Forecast Monte Carlo Experiment 
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  1. 1.
    Akaike, H.: A new look at the statistical model indentification. IEEE Transactions on Automatic Control 19, 716–723 (1974)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Box, G.E.P., Jenkins, G.M.: Time Series Analysis, Forecasting and Control. Holden Day, San Francisco (1976)MATHGoogle Scholar
  3. 3.
    Bock, H.H., Diday, E.: Analysis of Symbolic Data. Springer, Heidelberg (2000)Google Scholar
  4. 4.
    Billard, L., Diday, E.: Symbolic regression Analysis. In: Jajuga, K., et al. (eds.) Proceedings of the 8th Conference of the International Federation of Classification Societies, IFCS-2002, Crakow, Poland, pp. 281–288. Springer, Heidelberg (2002)Google Scholar
  5. 5.
    De Carvalho, F.A.T., Lima Neto, E.A., Tenorio, C.P.: A New Method to Fit a Linear Regression Model for Interval-Valued Data. In: Biundo, S., Frühwirth, T., Palm, G. (eds.) KI 2004. LNCS (LNAI), vol. 3238, pp. 295–306. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    Engle, R.F.: Autoregressive conditional heteroscedasticity with estimates of the variance of UK inflation. Econometrica 50, 987–1008 (1982)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks 2, 359–366 (1989)CrossRefGoogle Scholar
  8. 8.
    Tang, Z., Fishwick, P.A.: Feedforward neural nets as models for time series forecasting. ORSA Journal of Computing 5, 374–385 (1993)MATHGoogle Scholar
  9. 9.
    Zhang, G.: Time Series forecasting using a hybrid ARIMA and neural network model. Journal of Neurocomputing 50, 159–175 (2003)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • André Luis S. Maia
    • 1
  • Francisco de A.T. de Carvalho
    • 1
  • Teresa B. Ludermir
    • 1
  1. 1.Centro de Informatica – CIn/UFPERecifeBrazil

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