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Scaling and memory in the return intervals of realized volatility

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  • Fei Ren
  • Gao-Feng Gu
  • Wei-Xing Zhou
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    Abstract

    We perform return interval analysis of 1-min {\em{realized volatility}} defined by the sum of absolute high-frequency intraday returns for the Shanghai Stock Exchange Composite Index (SSEC) and 22 constituent stocks of SSEC. The scaling behavior and memory effect of the return intervals between successive realized volatilities above a certain threshold $q$ are carefully investigated. In comparison with the volatility defined by the closest tick prices to the minute marks, the return interval distribution for the realized volatility shows a better scaling behavior since 20 stocks (out of 22 stocks) and the SSEC pass the Kolmogorov-Smirnov (KS) test and exhibit scaling behaviors, among which the scaling function for 8 stocks could be approximated well by a stretched exponential distribution revealed by the KS goodness-of-fit test under the significance level of 5%. The improved scaling behavior is further confirmed by the relation between the fitted exponent $\gamma$ and the threshold $q$. In addition, the similarity of the return interval distributions for different stocks is also observed for the realized volatility. The investigation of the conditional probability distribution and the detrended fluctuation analysis (DFA) show that both short-term and long-term memory exists in the return intervals of realized volatility.

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    File URL: http://arxiv.org/pdf/0904.1107
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0904.1107.

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    Date of creation: Apr 2009
    Date of revision: Aug 2009
    Publication status: Published in Physica A 388 (2009) 4787-4796
    Handle: RePEc:arx:papers:0904.1107

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    References

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    1. Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 287(3), pages 468-481.
    2. Enrico Scalas & Rudolf Gorenflo & Francesco Mainardi, 2004. "Fractional calculus and continuous-time finance," Finance, EconWPA 0411007, EconWPA.
    3. Zhiguang (Gerald) Wang, 2009. "Volatility Risk," Issue Briefs, South Dakota State University, Department of Economics 2009513, South Dakota State University, Department of Economics.
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    Cited by:
    1. Luis A. Gil-Alana & Yun Cao, 2010. "Stock market prices in China. Efficiency, mean reversion, long memory volatility and other implicit dynamics," Faculty Working Papers, School of Economics and Business Administration, University of Navarra 12/11, School of Economics and Business Administration, University of Navarra.
    2. Ni, Xiao-Hui & Jiang, Zhi-Qiang & Gu, Gao-Feng & Ren, Fei & Chen, Wei & Zhou, Wei-Xing, 2010. "Scaling and memory in the non-Poisson process of limit order cancelation," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 389(14), pages 2751-2761.
    3. Jia, Zhanliang & Cui, Meilan & Li, Handong, 2012. "Research on the relationship between the multifractality and long memory of realized volatility in the SSECI," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 391(3), pages 740-749.
    4. Ouyang, F.Y. & Zheng, B. & Jiang, X.F., 2014. "Spatial and temporal structures of four financial markets in Greater China," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 402(C), pages 236-244.
    5. Xiao-Hui Ni & Zhi-Qiang Jiang & Gao-Feng Gu & Fei Ren & Wei Chen & Wei-Xing Zhou, 2009. "Scaling and memory in the non-poisson process of limit order cancelation," Papers 0911.0057, arXiv.org.
    6. 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, Elsevier, vol. 390(20), pages 3486-3495.
    7. He, Ling-Yun & Chen, Shu-Peng, 2011. "A new approach to quantify power-law cross-correlation and its application to commodity markets," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 390(21), pages 3806-3814.
    8. Wen-Jie Xie & Zhi-Qiang Jiang & Wei-Xing Zhou, 2012. "Extreme value statistics and recurrence intervals of NYMEX energy futures volatility," Papers 1211.5502, arXiv.org.
    9. F. Y. Ouyang & B. Zheng & X. F. Jiang, 2014. "Spatial and temporal structures of four financial markets in Greater China," Papers 1402.1046, arXiv.org.
    10. 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, Elsevier, vol. 391(22), pages 5546-5556.
    11. Xie, Wen-Jie & Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2014. "Extreme value statistics and recurrence intervals of NYMEX energy futures volatility," Economic Modelling, Elsevier, Elsevier, vol. 36(C), pages 8-17.

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