Using ARFIMA Model to Calculate and Forecast Realized Volatility of High Frequency Stock Market Index Data

  • Yulin Ma
  • Xia Li
  • Jing Zhao
  • Dengyue Luo
Part of the Advances in Intelligent Systems and Computing book series (volume 136)


The forecast precision of realized volatility can be affected by both measurement error and market microstructure error when we analyze volatility using high frequency data. This paper adopts the method of second moving average to balance these two errors and establishes ARFIMA model to study the distribution characteristics of realized volatility based on high frequency data of hushen300, its parameters are estimated applying estimation of distribution algorithm. Finally, the superiority of ARFIMA model in volatility forecast is proved by comparing the performances of ARFIMA model and GARCH model.


high frequency data realized volatility optimal sampling frequency ARFIMA model 


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  1. 1.
    Andersen, T.G., Bollerslev, T., et al.: The Distribution of Stock Return Volatility. Journal of Financial Economic 61, 43–76 (2001)CrossRefGoogle Scholar
  2. 2.
    Andersen, T.G., Bollerslev, T., et al.: Modelling and Forecasting Realized Volatility. Econometrica 71(2), 579–625 (2003)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Oomen Roel, C.A: Modelling realized variance when returns are series correlated (December 23, 2002),
  4. 4.
    Bollerslev, T., Wright, J.H.: Volatility Forecasting, High-Frequency Data, and Frequency Domain Inference. Review of Economic and Statistics 83, 596–602 (2001)CrossRefGoogle Scholar
  5. 5.
    Huang, H., Chen, L.: The high frequency estimation and characteristic analysis of Chinese stock market volatility. Economic Research Journal (2), 75–94 (2003)Google Scholar
  6. 6.
    Granger, C.W.J., Joyeux, R.: An Introduction to Long-memory Time Series Models and Fractional Differencing. Journal of Time Series Analysis (1), 15–29 (1980)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Hosking, J.R.M.: Fractional differencing. Biometrica 68(1), 165–176 (1981)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Geweke, J., Porter-Hudak, S.: The Estimation and Application of Long Memory Time Series Models. Journal of Time Series Analysis 4, 221–238 (1983)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Fleming, J., Kirby, C., Ostdiek, B.: The Economic Value of Volatility Time Using“Realized Volatility. Journal of Financial Economic 67, 473–509 (2003)CrossRefGoogle Scholar
  10. 10.
    Jin, X., Yao, J., Zhuang, X.: The study of ARFIMA model and forecasting effect based on fractional order difference. Mathematical Statistics and Management (9), 896–907 (2007)Google Scholar

Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.School of Statistic and MathematicsShandong University of Finance and EconomicsJinanChina
  2. 2.DongFang CollegeShandong University of Finance and EconomicsTaianChina
  3. 3.School of ManagementShandong UniversityJinanChina

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