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ARCH–GARCH approaches to modeling high-frequency financial data

Author

Listed:
  • Podobnik, Boris
  • Ivanov, Plamen Ch.
  • Grosse, Ivo
  • Matia, Kaushik
  • Eugene Stanley, H.

Abstract

We model the power-law stability in distribution of returns for S&P500 index by the GARCH process which we use to account for the long memory in the variance correlations. Precisely, we analyze the distributions corresponding to temporal aggregation of the GARCH process, i.e., the sum of n GARCH variables. The stability in the power-law tails is controlled by the GARCH parameters. We model the crossover behavior in magnitude correlations of returns by the so-called two-FIARCH process. Besides detrended fluctuation analysis, we employ the method proposed by Geweke and Porter-Hudak to estimate the fractional parameter in magnitude correlations.

Suggested Citation

  • Podobnik, Boris & Ivanov, Plamen Ch. & Grosse, Ivo & Matia, Kaushik & Eugene Stanley, H., 2004. "ARCH–GARCH approaches to modeling high-frequency financial data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 216-220.
    • Handle: RePEc:eee:phsmap:v:344:y:2004:i:1:p:216-220
    DOI: 10.1016/j.physa.2004.06.120
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    References listed on IDEAS

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    1. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871, January.
    2. Stanley, H.E. & Buldyrev, S.V. & Goldberger, A.L. & Goldberger, Z.D. & Havlin, S. & Mantegna, R.N. & Ossadnik, S.M. & Peng, C.-K. & Simons, M., 1994. "Statistical mechanics in biology: how ubiquitous are long-range correlations?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 205(1), pages 214-253.
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    Citations

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    Cited by:

    1. Stanley, H.E. & Gabaix, Xavier & Gopikrishnan, Parameswaran & Plerou, Vasiliki, 2007. "Economic fluctuations and statistical physics: Quantifying extremely rare and less rare events in finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 286-301.
    2. Kang, Sang Hoon & Yoon, Seong-Min, 2008. "Long memory features in the high frequency data of the Korean stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5189-5196.
    3. D’Urso, Pierpaolo & Cappelli, Carmela & Di Lallo, Dario & Massari, Riccardo, 2013. "Clustering of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 2114-2129.
    4. Lin, Xiaoqiang & Fei, Fangyu & Wang, Yudong, 2011. "Analysis of the efficiency of the Shanghai stock market: A volatility perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3486-3495.
    5. Gong, Xiaoli & Zhuang, Xintian, 2016. "Option pricing for stochastic volatility model with infinite activity Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 455(C), pages 1-10.
    6. Kang, Sang Hoon & Cheong, Chongcheul & Yoon, Seong-Min, 2013. "Intraday volatility spillovers between spot and futures indices: Evidence from the Korean stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(8), pages 1795-1802.
    7. Sun, Qi & Xu, Weidong, 2015. "Pricing foreign equity option with stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 89-100.
    8. Yoon, Seong-Min & Kang, Sang Hoon, 2009. "Weather effects on returns: Evidence from the Korean stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(5), pages 682-690.
    9. Stanley, H. Eugene & Plerou, Vasiliki & Gabaix, Xavier, 2008. "A statistical physics view of financial fluctuations: Evidence for scaling and universality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3967-3981.
    10. Lahmiri, Salim, 2017. "Asymmetric and persistent responses in price volatility of fertilizers through stable and unstable periods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 405-414.
    11. Wei, Yu, 2012. "Forecasting volatility of fuel oil futures in China: GARCH-type, SV or realized volatility models?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5546-5556.
    12. Kang, Sang Hoon & Yoon, Seong-Min, 2007. "Long memory properties in return and volatility: Evidence from the Korean stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 591-600.

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    Stochastic processes; Random walks;

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