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Scaling and memory in the return intervals of realized volatility

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

    We perform return interval analysis of 1-min 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 γ 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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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 388 (2009)
    Issue (Month): 22 ()
    Pages: 4787-4796

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    Handle: RePEc:eee:phsmap:v:388:y:2009:i:22:p:4787-4796

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Econophysics; Realized volatility; Return interval; Scaling; Long memory;

    References

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    1. Bernard Bollen & Brett Inder, 1999. "Estimating Daily Volatility in Financial Markets Utilizing Intraday Data," Working Papers 1999.01, School of Economics, La Trobe University.
    2. Scalas, Enrico & Kaizoji, Taisei & Kirchler, Michael & Huber, Jürgen & Tedeschi, Alessandra, 2006. "Waiting times between orders and trades in double-auction markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 463-471.
    3. Hsieh, David A, 1991. " Chaos and Nonlinear Dynamics: Application to Financial Markets," Journal of Finance, American Finance Association, vol. 46(5), pages 1839-77, December.
    4. Woo-Sung Jung & Fengzhong Wang & Shlomo Havlin & Taisei Kaizoji & Hie-Tae Moon & H. Eugene Stanley, 2007. "Volatility return intervals analysis of the Japanese market," Papers 0709.1725, arXiv.org.
    5. Bunde, Armin & F. Eichner, Jan & Havlin, Shlomo & W. Kantelhardt, Jan, 2004. "Return intervals of rare events in records with long-term persistence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(1), pages 308-314.
    6. Kantelhardt, Jan W & Koscielny-Bunde, Eva & Rego, Henio H.A & Havlin, Shlomo & Bunde, Armin, 2001. "Detecting long-range correlations with detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(3), pages 441-454.
    7. I. Vodenska-Chitkushev & F. Z. Wang & P. Weber & K. Yamasaki & S. Havlin & H. E. Stanley, 2008. "Comparison between volatility return intervals of the S&P 500 index and two common models," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 61(2), pages 217-223, 01.
    8. Jiang, Zhi-Qiang & Chen, Wei & Zhou, Wei-Xing, 2008. "Scaling in the distribution of intertrade durations of Chinese stocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5818-5825.
    9. Enrico Scalas & Rudolf Gorenflo & Francesco Mainardi & Maurizio Mantelli & Marco Raberto, 2003. "Anomalous waiting times in high-frequency financial data," Papers cond-mat/0310305, arXiv.org.
    10. Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2004. "Fractional calculus and continuous-time finance II: the waiting- time distribution," Finance 0411008, EconWPA.
    11. Bunde, Armin & F. Eichner, Jan & Havlin, Shlomo & Kantelhardt, Jan W., 2003. "The effect of long-term correlations on the return periods of rare events," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(1), pages 1-7.
    12. Qiu, T. & Guo, L. & Chen, G., 2008. "Scaling and memory effect in volatility return interval of the Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(27), pages 6812-6818.
    13. Zhi-Qiang Jiang & Wei Chen & Wei-Xing Zhou, 2008. "Scaling in the distribution of intertrade durations of Chinese stocks," Papers 0804.3431, arXiv.org, revised Apr 2008.
    14. Taisei Kaizoji & Michiyo Kaizoji, 2003. "Power law for ensembles of stock prices," Papers cond-mat/0312406, arXiv.org, revised Mar 2006.
    15. C. Pennetta, 2006. "Distribution of return intervals of extreme events," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 50(1), pages 95-98, 03.
    16. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    17. Tian Qiu & Liang Guo & Guang Chen, 2008. "Scaling and Memory Effect in Volatility Return Interval of the Chinese Stock Market," Papers 0805.2194, arXiv.org.
    18. F. Wang & P. Weber & K. Yamasaki & S. Havlin & H. E. Stanley, 2007. "Statistical regularities in the return intervals of volatility," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 55(2), pages 123-133, 01.
    19. Ren, Fei & Guo, Liang & Zhou, Wei-Xing, 2009. "Statistical properties of volatility return intervals of Chinese stocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 881-890.
    20. Fei Ren & Wei-Xing Zhou, 2008. "Multiscaling behavior in the volatility return intervals of Chinese indices," Papers 0809.0250, arXiv.org.
    21. Plamen Ch. Ivanov & Ainslie Yuen & Boris Podobnik & Youngki Lee, 2004. "Common Scaling Patterns in Intertrade Times of U. S. Stocks," Papers cond-mat/0403662, arXiv.org.
    22. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
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    Citations

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    Cited by:
    1. 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.
    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, vol. 389(14), pages 2751-2761.
    3. Xie, Wen-Jie & Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2014. "Extreme value statistics and recurrence intervals of NYMEX energy futures volatility," Economic Modelling, Elsevier, vol. 36(C), pages 8-17.
    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, vol. 402(C), pages 236-244.
    5. 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.
    6. 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.
    7. 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.
    8. 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, vol. 391(3), pages 740-749.
    9. 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, vol. 390(21), pages 3806-3814.
    10. 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.
    11. 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 12/11, School of Economics and Business Administration, University of Navarra.

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