Prediction of Long-Range Dependent Time Series Data with Performance Guarantee

  • Mikhail Dashevskiy
  • Zhiyuan Luo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5792)


Modelling and predicting long-range dependent time series data can find important and practical applications in many areas such as telecommunications and finance. In this paper, we consider Fractional Autoregressive Integrated Moving Average (FARIMA) processes which provide a unified approach to characterising both short-range and long-range dependence. We compare two linear prediction methods for predicting observations of FARIMA processes, namely the Innovations Algorithm and Kalman Filter, from the computational complexity and prediction performance point of view. We also study the problem of Prediction with Expert Advice for FARIMA and propose a simple but effective way to improve the prediction performance. Alongside the main experts (FARIMA models) we propose to use some naive methods (such as Least-Squares Regression) in order to improve the performance of the system. Experiments on publicly available datasets show that this construction can lead to great improvements of the prediction system. We also compare our approach with a traditional method of model selection for the FARIMA model, namely Akaike Information Criterion.


Akaike Information Criterion Kalman Filter ARMA Model Expert Advice Naive Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Bisaglia, L.: Model selection for long-memory models. Quaderni di Statistica 4 (2002)Google Scholar
  2. 2.
    Blok, H.J.: On The Nature Of The Stock Market: Simulations And Experiments. PhD Thesis, University of British Columbia, Canada (2000)Google Scholar
  3. 3.
    Brockwell, P.J., Davis, R.A.: Time Series: Theory and Methods. Springer, Heidelberg (1991)CrossRefzbMATHGoogle Scholar
  4. 4.
    Dashevskiy, M., Luo, Z.: Guaranteed Network Traffic Demand Prediction Using FARIMA Models. In: Fyfe, C., Kim, D., Lee, S.-Y., Yin, H. (eds.) IDEAL 2008. LNCS, vol. 5326, pp. 274–281. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  5. 5.
    Dethe, C.G., Wakde, D.G.: On the prediction of packet process in network traffic using FARIMA time-series model. J. of Indian Inst. of Science 84, 31–39 (2004)Google Scholar
  6. 6.
    Granger, C.W.J., Joyeux, R.: An introduction to long-memory time series models and fractional differencing. J. of Time Series Analysis 1, 15–29 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Hosking, J.R.M.: Fractional differencing. Biometrica 68, 165–176 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    de Jong, P., Penzer, J.: The ARMA model in state space form. Statistics & Probability Letters 70(1), 119–125 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Kalman, R.E.: A new approach to linear filtering and prediction problems. Journal of Basic Engineering 82, 34–45 (1960)Google Scholar
  10. 10.
    Kalman, R.E., Bucy, R.S.: New results in linear filtering and prediction theory. Journal of Basic Engineering 83, 95–108 (1961)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Laurencelle, L., Dupuis, F.-A.: Statistical Tables, Explained and Applied: Explained and Applied. World Scientific, Singapore (2002)CrossRefzbMATHGoogle Scholar
  12. 12.
    Leland, W.E., Taqqu, M.S., Willinger, W., Wilson, D.V.: On the self-similar nature of Ethernet traffic. IEEE/ACM Trans. on Networking. 2, 1–15 (1994)CrossRefGoogle Scholar
  13. 13.
    de Lima, A.B., de Amazonas, J.R.A.: State-space Modeling of Long-Range Dependent Teletraffic. In: Mason, L.G., Drwiega, T., Yan, J. (eds.) ITC 2007. LNCS, vol. 4516, pp. 260–271. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  14. 14.
    Palmo, W.: Long-Memory Time Series. Theory and Methods. Wiley Series in Probability and Statistics (2007)Google Scholar
  15. 15.
    Paxson, V.: Fast Approximation of Self-Similar Network Traffic. Technical report LBL-36750/UC-405 (1995)Google Scholar
  16. 16.
    Shu, Y., Jin, Z., Zhang, L., Wang, L., Yang, O.W.W.: Traffic prediction using FARIMA models. In: IEEE International Conf. on Communication, vol. 2, pp. 891–895 (1999)Google Scholar
  17. 17.
    Taqqu, M.S., Teverovsky, V., Willinger, W.: Estimators for long-range dependence: An empirical study. Fractals 3, 785–788 (1995)CrossRefzbMATHGoogle Scholar
  18. 18.
    Vovk, V.: Competitive On-line Statistics. Int. Stat. Review 69, 213–248 (2001)CrossRefzbMATHGoogle Scholar
  19. 19.
    Vovk, V.: Prediction with expert advice for the Brier game (2008),
  20. 20.
    Willinger, W., Paxson, V., Riedi, R.H., Taqqu, M.S.: Long-range dependence and data network traffic. Theory And Applications Of Long-Range Dependence, 373–407 (2003)Google Scholar
  21. 21.
    Xue, F.: Modeling and Predicting Long-range Dependent Traffic with FARIMA Processes. In: Proc. of 1999 International Symposium on Communication (1999)Google Scholar
  22. 22.
    Xue, F., Liu, J., Zhang, L., Yang, O.W.W.: Traffic Modelling Based on FARIMA Models. In: Proc. IEEE Canadian Conference on Electrical and Computer Eng. (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Mikhail Dashevskiy
    • 1
  • Zhiyuan Luo
    • 1
  1. 1.Computer Learning Research CentreRoyal Holloway, University of LondonEghamUK

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