GARCH prediction using spline wavelet support vector machine

Original Article

Abstract

Volatility forecasting is vital important in finance to reduce risk and take better decisions. This paper proposes a spline wavelet support vector machine (SWSVM) to forecast the volatility of financial time series based on generalized autoregressive conditional heteroscedasticity model. An admissible spline wavelet kernel is constructed by incorporating the wavelet technique and spline theory into support vector machine (SVM). Since spline wavelet function can yield features that describe the stock time series both at various locations and at varying time granularities, the SWSVM gains the cluster feature of volatility well. Compared with Gaussian kernel in the standard SVM, the applicability and validity of spline wavelet kernel in SWSVM are confirmed through computer simulations and experiments on real-world stock data.

Keywords

Volatility forecasting GARCH Spline wavelet support vector machine 

References

  1. 1.
    Engle RF (1982) Autoregressive conditional heteroskedasticity with estimates of the variance of UK inflation. Econometrica 50:987–1008. doi:10.2307/1912773 MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bollerslev T (1986) A generalized autoregressive conditional heteroskedasticity. J Econom 31:307–327. doi:10.1016/0304-4076(86)90063-1 MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Day TE, Lewis CM (1998) The behavior of the volatility implicit in the prices of stock index options. J Financ Econ 22:103–122. doi:10.1016/0304-405X(88)90024-4 CrossRefGoogle Scholar
  4. 4.
    Franses PH, van Dijk D (1996) Forecasting stock market volatility using (nonlinear) GARCH models. J Forecast 15:229–235. doi:10.1002/(SICI)1099-131X(199604)15:3<229::AID-FOR620>3.0.CO;2-3CrossRefGoogle Scholar
  5. 5.
    Harvey CR, Whaley RE (1991) S&P100 index option volatility. J Finance 46:1551–1561. doi:10.2307/2328872 CrossRefGoogle Scholar
  6. 6.
    Hull J, White A (1987) The pricing of options on assets with stochastic volatilities. J Finance 42:281–300. doi:10.2307/2328253 CrossRefGoogle Scholar
  7. 7.
    Li WK, Mak TK (1994) On the squared residual autocorrelations in nonlinear time series with conditional heteroskedasticity. J Time Ser Anal 15:627–636. doi:10.1111/j.1467-9892.1994.tb00217.x MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Poterba JM, Summers LH (1986) The persistence of volatility and stock market fluctuations. Am Econ Rev 76:1142–1151Google Scholar
  9. 9.
    Perez-Cruz F, Afonso-Rodriguez JA, Giner J (2003) Estimating GARCH models using support vector machines. Quant Finance 3(3):163–172CrossRefMathSciNetGoogle Scholar
  10. 10.
    Smola AJ, Schölkopf BA (1998) Tutorial on support vector regression. NeuroCOLT technical report NC-TR-98-030. Royal Holloway College, LondonGoogle Scholar
  11. 11.
    Vapnik VN (1995) The nature of statistical learning theory. Springer, New YorkMATHGoogle Scholar
  12. 12.
    Vapnik VN (1998) Statistical learning theory. Wiley, New YorkMATHGoogle Scholar
  13. 13.
    Schölkopf B, Burges CJC, Smola AJ (1999) Advances in kernel methods. The MIT Press, LondonGoogle Scholar
  14. 14.
    Daubechies I (1990) The wavelet transform: time-frequency localization and signal analysis. IEEE Trans Inform Theory 36(5):961–1005. doi:10.1109/18.57199 MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Daubechies I (1992) Ten lectures on wavelets. SIAM, PhiladelphiaMATHGoogle Scholar
  16. 16.
    Mallat S (1998) A theory for muliresolution signal decomposition: The wavelet representation. IEEE Trans Pattern Anal Mach Intell 11:674–693. doi:10.1109/34.192463 CrossRefGoogle Scholar
  17. 17.
    Mallat S (1998) A wavelet tour of signal processing. Academic Press, BostonMATHGoogle Scholar
  18. 18.
    Chui CK (1992) An introduction to wavelets. Academic Press, LondonGoogle Scholar
  19. 19.
    Chui CK (1997) Wavelets: a mathematical tool for signal analysis. SIAM, PhiladelphiaGoogle Scholar
  20. 20.
    Zavjalov YS, Kvasov BI, Miroshnicenko VL (1980) Spline function methods. Nauka, MoscowGoogle Scholar
  21. 21.
    Kaastra I, Boyd M (1996) Designing a neural network for forecasting financial and economic time series. Neurocomputing 10(3):215–236. doi:10.1016/0925-2312(95)00039-9 CrossRefGoogle Scholar
  22. 22.
    Montgomery DC, Runger GC (1999) Applied statistics and probability for engineers. Wiley & Sons, New YorkGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2009

Authors and Affiliations

  • Ling-Bing Tang
    • 1
    • 2
  • Huan-Ye Sheng
    • 1
  • Ling-Xiao Tang
    • 3
  1. 1.Department of Computer Science and EngineeringShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Department of Computer and Electronic EngineeringHunan Business CollegeChangshaChina
  3. 3.School of EconomicsChangsha University of Science and TechnologyChangshaChina

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