Skip to main content

A Novel Technique for ARMA Modelling with Order and Parameter Estimation Using Genetic Algorithms

  • Conference paper
  • 1169 Accesses

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 88))

Abstract

A new method for determining simultaneously the order and parameters of Auto Regressive Moving Average (ARMA) models is presented in this paper. ARMA models, which can be present in different fields such as communication systems, control systems, internet software and hardware models are determined using genetic algorithms (GAs). Given ARMA (p, q) model input/output data with the absence of any information about the order, the correct model (p, q) is determined (order and parameters). The proposed method works on the principle of minimizing the overall deviation between the actual plant output, with or without noise, and the estimated plant output. The algorithm does not use complex mathematical procedures in its detection. Simulation results covered in this paper show in detail the efficiency and the generality of the proposed approach. In addition to that, the new method is compared with other well known methods for ARMA model order and parameter estimation.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Sayood, K., Schekall, S.M.: Use of ARMA Predictors in the Differential Encoding of Images. IEEE Transactions on Acoustics, Speech and Signal Processing 36, 1791–1795 (1988)

    Article  MATH  Google Scholar 

  2. Celenk, M., Conley, T., Graham, J., Willis, J.: Anomaly prediction in network traffic using adaptive Wiener filtering and ARMA modeling. In: IEEE International Conference on Systems, Man and Cybernetics, pp. 3548–3553 (2008)

    Google Scholar 

  3. Cricenti, A., Branch, P.: ARMA (1,1) Modeling of Quake4 Server to Client Game Traffic. In: Proceedings of the 6th ACM SIGCOMM Workshop on Network and System Support for Games, Nelbourne, Australia, pp. 70–74 (2007)

    Google Scholar 

  4. Zito, G., Landau, I.D.: Digital Control Systems - design, identification, implementation. Springer, London (2006)

    Google Scholar 

  5. Al-Smadi, A., Al-Zaben, A.: ARMA Model Order Determination Using Edge Detection: A New Perspective. Circuit Systems Signal Processing 24, 723–732 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  6. Broersen, P.M.: Automatic Autocorrelation and Spectral Analysis. Springer, London (2006)

    Google Scholar 

  7. Akaike, H.: Fitting autoregressive models for prediction. Ann. Znst. Sat. Math. 21, 243–247 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  8. Akaike, H.: Statistical predictor identification. Ann. Znst. Stat. Math. 22, 203–217 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  9. Hannan, E.J.: The estimation of the order of an ARMA process. Ann. Stat. 8(5), 1071–1081 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  10. Rissanen, J.: Modeling by shortest data description. Automatica 14, 465–471 (1978)

    Article  MATH  Google Scholar 

  11. Liang, G., Wilkes, D.M., Cadzow, J.A.: ARMA model order estimation based on the eigenvalues of the covariance matrix. IEEE Trans. Signal Processing 41, 3003–3009 (1993)

    Article  MATH  Google Scholar 

  12. Chang, W.D.: Coefficient Estimation of IIR Filter by a Multiple Crossover Genetic Algorithm. Computers and Mathematics with Applications 51, 1437–1444 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  13. Rolf, S., Sprave, J., Urfer, W.: Model Identification and Parameter Estimation of ARMA Models by Means of evolutionary Algorithms. Computational Intelligence for Financial Engineering 23, 237–243 (1997)

    Google Scholar 

  14. Peng, P., Chen, Q.: Improved Genetic Algorithm and Application to ARMA Modelling. In: SICE Annual Conference, vol. 1, pp. 134–139. Fukui University, Japan (2003)

    Google Scholar 

  15. Al-Smadi, A.: Automatic identification of ARMA systems. International Journal of General Systems 38(1), 29–41 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  16. Abo-Hammour, Z.S., Yusuf, M., Mirza, N.M., Mirza, S.M., Arif, M., Khurshid, J.: Numerical solution of second-order, two-point boundary value problems using continuous genetic algorithms. International Journal for Numerical Methods in Engineering 61, 1219–1242 (2004)

    Article  MATH  Google Scholar 

  17. Warwick, K., Kang, Y.H.: Self-tuning proportional integral and derivative controller based on genetic algorithm least squares. Proceedings of the Institution of Mechanical Engineers Part I-Journal of Systems and Control Engineering 212, 437–448 (1998)

    Article  Google Scholar 

  18. Nissinen, A.S., Koivo, H.N., Koivisto, H.: Optimization of neural network topologies using genetic algorithm. Intelligent Automation and Soft Computing 5, 211–223 (1999)

    Google Scholar 

  19. Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, New York (1989)

    MATH  Google Scholar 

  20. Michalewics, Z.: Genetic Algorithms + Data Structure = Evolution Programs. Springer, New York (1996)

    Google Scholar 

  21. Haupt, R.L., Haupt, S.E.: Practical Genetic Algorithms. John Wiley & Sons, New Jersey (2004)

    MATH  Google Scholar 

  22. Chen, S.M.: Automatically Constructing Membership Functions and Generating Fuzzy Rules using Genetic Algorithms. An International Journal 33, 841–862 (2002)

    Google Scholar 

  23. Abo-Hammour, Z.S.: Advanced Continuous Genetic Algorithm and Their Application in the Motion Planning of Robot Manipulators and in the Numerical Solution of Boundary Value Problems. Ph.D thesis. Quaid-i-Azam University, Islamabad (2002)

    Google Scholar 

  24. Ljung, L.: System Identification Toolbox for use with MATLAB, Version 5, 5th edn. The Math-Works Inc., Natick (2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Abo-Hammour, Z.S., Alsmadi, O.M.K., Al-Smadi, A.M. (2010). A Novel Technique for ARMA Modelling with Order and Parameter Estimation Using Genetic Algorithms. In: Zavoral, F., Yaghob, J., Pichappan, P., El-Qawasmeh, E. (eds) Networked Digital Technologies. NDT 2010. Communications in Computer and Information Science, vol 88. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14306-9_56

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14306-9_56

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14305-2

  • Online ISBN: 978-3-642-14306-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics