Paper:

# A Hybrid System ASVR/NGARCH Tuned by Quantum-Based Minimization to Improve Forecasting Accuracy

## Bao Rong Chang

Department of Computer Science and Information Engineering, National Taitung University, 684 Chunghua Rd., Sec. 1, Taitung City, Taitung, Taiwan

Adaptive support vector regression (ASVR) is very useful to act as a predictor for complex time series prediction. However, ASVR cannot avoid volatility clustering and thus worsen its predictive accuracy. Therefore, incorporating NGARCH model into ASVR is schemed for resolving the problem of volatility clustering to best fit the time series. Interestingly, quantum-based minimization algorithm is proposed in this study to tune the resulting weighted-average forecasts between ASVR and NGARCH to improve the forecast performance. Quantum optimization process tackles so-called NP-completeness problem outperforming artificial neural network or quadratic-programming so as to attain optimal or near-optimal result over the scope of search space. It follows that the proposed hybrid system can get the satisfactory results because of highly enhancing its generalization and then improving the accuracy.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.11, No.4, pp. 381-388, 2007.

- [1] B. R. Chang and S. F. Tsai, “Adaptive Support Vector Regression,” Proc. of International Computer Symposium, Taipei, Taiwan, pp. 901-907, 2004.
- [2] T. Bellerslve, “Generalized Autoregressive Conditional Heteroscedasticity,” Journal of Econometrics, Vol.31, pp. 307-327, 1986.
- [3] M. A. Nielsen and I. L. Chuang, “Quantum computation and quantum information,” Cambridge University Press, London, ISBN 0521 63503 9, 2000.
- [4] G. E. P. Box, G. M. Jenkins, and G. C. Reinsel, “Time Series Analysis: Forecasting & Control,” Prentice-Hall, New Jersey, 1994.
- [5] J. L. Deng, “Control Problems of Grey System,” System and Control Letter, Vol.1, No.5, pp. 288-294, 1982.
- [6] B. R. Chang, “A Study of Non-Periodic Short-Term Random Walk Forecasting Based on RBFNN, ARMA, or SVR-GM(1,1,tau) Approach,” Proc. of IJCNN, pp. 254-259, 2003.
- [7] V. Vapnik, “The Nature of Statistical Learning Theory,” Springer-Verlag, New York, 1995.
- [8] C. Gourieroux, “ARCH Models and Financial Applications,” Springer-Verlag, New York, 1997.
- [9] D. Anguita, S. Ridella, F. Rivieccio, and R. Zunino, “Training Support Vector Machines: a Quantum-Computing Perspective,” Proc. IEEE IJCNN, pp. 1587-1592, 2003.
- [10] R. Fletcher, “Practical Methods of Optimization (2nd Ed.),” Wiley and Sons, New York, 1987.
- [11] D. Deutsch and R. Jozsa, “Rapid solution of problems by quantum computation,” Pro. of the Royal Society, London, A439, pp. 553-558, 1992.
- [12] L. K. Grover, “A Fast Quantum Mechanical Algorithm for Database Search,” Proc. 28th Ann. ACM Symp. Theory of Comp., ACM Press, pp. 212-219, 1996.
- [13] C. Durr and P. Hoyer, “A Quantum Algorithm for Finding the Minimum,”

http://arxiv.org/abs/quant-ph/9607014. - [14] M. Boyer, G. Brassard, P. Hoyer, and A. Tapp, “Tight Bounds on Quantum Searching,” Fortschritte Der Physik, 1998.
- [15] V. Vapnik, “The nature of statistical learning theory,” Springer-Verlag, New York, 1995.
- [16] N. Cristianini and J. Shawe-Taylor, “An Introduction to Support Vector Machines,” Cambridge University Press, London, 2000.
- [17] E. Kreyszig, “Advanced Engineering Mathematics,” 8th Edition, Wiley, New York, 1999.
- [18] J. D. Hamilton, “Time Series Analysis,” Princeton University Press, New Jersey, 1994.
- [19] L. Hentschel, “All in the Family: Nesting Symmetric and Asymmetric GARCH Models,” Journal of Financial Economics, Vol.39, pp. 71-104, 1995.
- [20] B. N. Pshenichnyj and S. S. Wilson, “The Linearization Method for Constrained Optimization,” Springer, New York, 1994.
- [21] I. Ono and S. Kobayashi, “A Real-coded Genetic Algorithm for Function Optimization Using Unimodal Normal Distribution Crossover,” Proc. 7th International Conf. on Genetic Algorithms, pp. 246-253, 1997.
- [22] International Stock Price Index, FIBV FOCUS MONTHLY STATISTICS, 2005.
- [23] G. M. Ljung and G. E. P. Box, “On a Measure of Lack of Fit in Time Series Models,” Biometrika, Vol.65, pp. 67-72, 1978.
- [24] Typhoon Moving Trace Inquire, Central Weather Bureau, Taipei, Taiwan, 2005.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 International License.