# Scaling and memory in the return intervals of realized volatility

## Author Info

• 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

## Bibliographic Info

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

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 Length: 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 Contact details of provider: Web page: http://arxiv.org/

## References

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1. Enrico Scalas & Rudolf Gorenflo & Francesco Mainardi, 2000. "Fractional calculus and continuous-time finance," Papers cond-mat/0001120, arXiv.org.
2. Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Papers cond-mat/0006454, arXiv.org, revised Nov 2000.
3. Zhiguang (Gerald) Wang, 2009. "Volatility Risk," Issue Briefs 2009513, South Dakota State University, Department of Economics.
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