Artificial Neural Network-Based Algorithm for ARMA Model Order Estimation

  • Khaled E. Al-Qawasmi
  • Adnan M. Al-Smadi
  • Alaa Al-Hamami
Part of the Communications in Computer and Information Science book series (CCIS, volume 88)


This paper presents a new algorithm for the determination of the Autoregressive Moving Average (ARMA) model order based on Artificial Neural Network (ANN). The basic idea is to apply ANN to a special matrix constructed from the Minimum Eginevalue (MEV) criterion. The MEV criterion is based on a covariance matrix derived from the observed output data only. The input signal is unobservable. The proposed algorithm is based on training the MEV covariance matrix dataset using the back-propagation technique. Our goal is to develop a system based on ANN; hence, the model order can be selected automatically without the need of prior knowledge about the model or any human intervention. Examples are given to illustrate the significant improvement results.


Artificial Neural Networks ANN ARMA Back-Propagation Simulation Eginevalue System Identification Signal Processing Time Series 


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  1. 1.
    Chen, Y.W., Chou, C.-C.: Correlation based Traffic Modeling of Sub-networks. Journal of Internet Technology, 277–283 (October 2003)Google Scholar
  2. 2.
    Akaike, H.: Fitting autoregressive models for prediction. Ann. Inst. Stat. Math. 21, 243–247 (1969)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Akaike, H.: Statistical Predictor Identification. Ann. Inst. Statist. Math., 203–217Google Scholar
  4. 4.
    Akaike, H.: A new look at statistical model identification. IEEE Trans. Automat. Contr. AC-19, 716–723 (1974/1970)Google Scholar
  5. 5.
    Al-Qawasmi, K., Al-Smadi, A., Al-Hamami, A.: A Robust ARX and ARMA Model Order Estimation via Pivot-Neighbors Comparisons. Recent Patents on Computer Science 3, 33–38 (2010)CrossRefGoogle Scholar
  6. 6.
    Al-Smadi, A.: A least-squares-based algorithm for identification of non-Gaussian ARMA models. Cir. Sys. Sig. Proc. 26(5), 715–731 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Al-Smadi, A.: Automatic identification of ARMA processes. Inter. J. Gen. Sys. 38, 29–41 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Al-Smadi, A., Wilkes, D.M.: Robust and accurate ARX and ARMA model order estimation of non-Gaussian Process. IEEE Trans. Signal Process. 50(3), 759–763 (2002)CrossRefGoogle Scholar
  9. 9.
    Cigizoglu, H.K.: Incorporation of ARMA Models into Flow Forecasting by Artificial Neural Networks. Environmetrics 14, 417–427 (2003)CrossRefGoogle Scholar
  10. 10.
    Demuth, H., Beale, M.: Neural Network Toolbox For Use with MATLAB, Version 5. The Math. Works, Inc. (2007)Google Scholar
  11. 11.
    Fausett, L.: Fundamentals of Neural Networks: Architectures, Algorithms and Applications. Prentice Hall, New Jersey (1994)zbMATHGoogle Scholar
  12. 12.
    Groupe, D.: Principles of Artificial Neural Networks, 2nd edn. World Scientific Publishing, New Jersey (2007)Google Scholar
  13. 13.
    Hannan, E.J.: The estimation of the order of an ARMA process. Ann. Stat. 8 (1980)Google Scholar
  14. 14.
    Khashei, M., Bijari, M., Ardali, G.A.: Improvement of Auto-Regressive Integrated Moving Average Models Using Fuzzy Logic and Artificial Neural Networks (ANNs). Neurocomputing 72, 956–967 (2009)CrossRefGoogle Scholar
  15. 15.
    Liang, G., Wilkes, D.M., Cadzow, J.A.: ARMA model order estimation based on the eigenvalues of the covariance matrix. IEEE Trans. on Signal Proc. 41(10), 3003–3009 (1993)zbMATHCrossRefGoogle Scholar
  16. 16.
    Rissanen, J.: Modeling by shortest data description. Automatica 14, 465–471 (1978)zbMATHCrossRefGoogle Scholar
  17. 17.
    Rojas, I., Valenzuela, O., Rojas, F., Guillen, A., Herrera, L.J., Pomares, H., Marquez, L., Pasadas, M.: Soft-computing techniques and ARMA model for time series prediction. Neurocomputing 71, 519–537 (2008)CrossRefGoogle Scholar
  18. 18.
    Schwarz, G.: Estimation of the dimension of a model. Ann. Stat. 6(2), 461–464 (1978)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Khaled E. Al-Qawasmi
    • 1
  • Adnan M. Al-Smadi
    • 2
  • Alaa Al-Hamami
    • 1
  1. 1.Depatrment of Computer Science,College of Information TechnologyAmman Arab University for Graduate StudiesAmmanJordan
  2. 2.Depatrment of Computer Science, College of Information TechnologyAl Al-Bayt UniversityAl-MafraqJordan

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