Novel Prediction Approach – Quantum-Minimum Adaptation to ANFIS Outputs and Nonlinear Generalized Autoregressive Conditional Heteroscedasticity

  • Bao Rong Chang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4223)


Volatility clustering degrades the efficiency and effectiveness of time series prediction and gives rise to large residual errors. This is because volatility clustering suggests a time series where successive disturbances, even if uncorrelated, are yet serially dependent. To overcome volatility clustering problems, an adaptive neuro-fuzzy inference system (ANFIS) is combined with a nonlinear generalized autoregressive conditional heteroscedasticity (NGARCH) model that is adapted by quantum minimization (QM) so as to tackle the problem of time-varying conditional variance in residual errors. The proposed method significantly reduces large residual errors in forecasts because volatility clustering effects are regulated to trivial levels. Two experiments using real financial data series compare the proposed method and a number of well-known alternative methods. Results show that forecasting performance by the proposed method produces superior results, with good speed of computation. Goodness of fit of the proposed method is tested by Ljung-Box Q-test. It is concluded that the ANFIS/NGARCH composite model adapted by QM performs very well for improved predictive accuracy of irregular non-periodic short-term time series forecast and will be of interest to the science of statistical prediction of time series.


Mean Square Error Mean Absolute Percent Error Mean Absolute Deviation Grey Model Volatility Cluster 
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  1. 1.
    Chang, B.R.: Advanced Hybrid Prediction Algorithm for Non-Periodic Short-Term Forecasting. International Journal of Fuzzy System 5(3), 151–160 (2003)Google Scholar
  2. 2.
    Box, G.E.P., Jenkins, G.M., Reinsel, G.C.: Time Series Analysis: Forecasting & Control. Prentice-Hall, New Jersey (1994)MATHGoogle Scholar
  3. 3.
    Chang, B.R.: Tuneable Free Parameters C and Epsilon-Tube in Support Vector Regression Grey Prediction Model -SVRGM(1,1|C,ε) Approach. In: Proc. IEEE International Conference on Systems, Man, and Cybernetics, pp. 2431–2437 (2004)Google Scholar
  4. 4.
    Castillo, O., Melin, P.: Simulation and Forecasting Complex Economic Time Series Using Neural Network and Fuzzy Logic. In: Proc. International Joint Conference on Neural Network, pp. 1805–1810 (2001)Google Scholar
  5. 5.
    Thomson, R., Hodgman, T.C., Yang, Z.R., Doyle, A.K.: Characterizing Proteolytic Cleavage Site Activity Using Bio-Basis Function Neural Networks. Bioinformatics 19(14), 1741–1747 (2003)CrossRefGoogle Scholar
  6. 6.
    Chang, B.R.: Hybrid BPNN-Weighted Grey-CLMS Forecasting. Journal of Information Science and Engineering 21(1), 209–221 (2005)Google Scholar
  7. 7.
    Jang, J.-S.R.: ANFIS: Adaptive-Network-based Fuzzy Inference Systems. IEEE Transactions on Systems, Man, and Cybernetics 23(3), 665–685 (1993)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Wang, J.-S.: An Efficient Recurrent Neuro-Fuzzy System for Identification and Control of Dynamic Systems. In: Proc. IEEE International Conference on Systems, Man, and Cybernetics, tracking #: 146 (2003)Google Scholar
  9. 9.
    Neter, J., Wasserman, W., Kutner, M.H.: Applied Linear Statistical Models, 2nd edn. Irwin, Homewood, IL (1985)Google Scholar
  10. 10.
    Bellerslve, T.: Generalized Autoregressive Conditional Heteroscedasticity. Journal of Econometrics 31, 307–327 (1986)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Gourieroux, C.: ARCH Models and Financial Applications. Springer, New York (1997)MATHGoogle Scholar
  12. 12.
    Durr, C., Hoyer, P.: A Quantum Algorithm for Finding the Minimum (1996),
  13. 13.
    Hamilton, J.D.: Time Series Analysis. Princeton University Press, New Jersey (1994)MATHGoogle Scholar
  14. 14.
    Pshenichnyj, B.N., Wilson, S.S.: The Linearization Method for Constrained Optimization. Springer, New York (1994)MATHGoogle Scholar
  15. 15.
    Boyer, M., Brassard, G., Hoyer, P., Tapp, A.: Tight Bounds on Quantum Searching. Fortschritte Der Physik (1998)Google Scholar
  16. 16.
    Grover, L.K.: A Fast Quantum Mechanical Algorithm for Database Search. In: Proc. 28th Ann. ACM Symp. Theory of Comp., pp. 212–219. ACM Press, New York (1996)Google Scholar
  17. 17.
    Anguita, D., Ridella, S., Rivieccio, F., Zunino, R.: Training Support Vector Machines: a Quantum- Computing Perspective. In: Proc. IEEE IJCNN, pp. 1587–1592 (2003)Google Scholar
  18. 18.
    Diebold, F.X.: Elements of Forecasting. South-Western, Cincinnati (1998)Google Scholar
  19. 19.
    FIBV FOCUS MONTHLY STATISTICS, International Stock Price Index (2005)Google Scholar
  20. 20.
    Ljung, G.M., Box, G.E.P.: On a Measure of Lack of Fit in Time Series Models. Biometrika 65, 67–72 (1978)CrossRefGoogle Scholar
  21. 21.
    London International Financial Futures and Options Exchange (LIFFE) (2002),

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Bao Rong Chang
    • 1
  1. 1.Department of Computer Science and Information EngineeringNational Taitung UniversityTaitungTaiwan

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