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摘要翻译：
本文详细研究了30只中国流通股连续1min波动率超过一定阈值($q$)之间的收益率区间($\tau_q$)的统计性质。Kolmogorov-Smirnov(KS)检验表明，对于不同的阈值$q$，12只股票在$\tau_q$分布上表现出标度行为。KS检验和加权KS检验表明，在5%的显著性水平下，有6只股票（12只股票中的6只股票）的标度收益区间分布可以很好地拟合为一个伸展指数函数$F(\tau/\bar{\tau}）\sim e^{-\alpha(\tau/\bar{\tau}）^{\gamma}}$,其中$\bar{\tau}$为平均收益区间，约为0.31$。通过对条件概率分布$P_q(\tau\tau_0)$和平均条件收益率区间$<\tau\tau_0>$的研究，证明了连续收益率区间区间之间存在短期相关性。我们进一步研究了一组$n$区间后的平均收益区间$<\tau\tau_0>$和波动$f(l)$,发现波动收益区间也存在长期记忆。
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英文标题：
《Statistical properties of volatility return intervals of Chinese stocks》
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作者：
Fei Ren, Liang Guo, and Wei-Xing Zhou
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最新提交年份：
2008
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Physics 物理学
二级分类：Data Analysis, Statistics and Probability 数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
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一级分类：Physics 物理学
二级分类：Physics and Society 物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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英文摘要：
The statistical properties of the return intervals $\tau_q$ between successive 1-min volatilities of 30 liquid Chinese stocks exceeding a certain threshold $q$ are carefully studied. The Kolmogorov-Smirnov (KS) test shows that 12 stocks exhibit scaling behaviors in the distributions of $\tau_q$ for different thresholds $q$. Furthermore, the KS test and weighted KS test shows that the scaled return interval distributions of 6 stocks (out of the 12 stocks) can be nicely fitted by a stretched exponential function $f(\tau/\bar{\tau})\sim e^{- \alpha (\tau/\bar{\tau})^{\gamma}}$ with $\gamma\approx0.31$ under the significance level of 5%, where $\bar{\tau}$ is the mean return interval. The investigation of the conditional probability distribution $P_q(\tau | \tau_0)$ and the mean conditional return interval $<\tau| \tau_0>$ demonstrates the existence of short-term correlation between successive return interval intervals. We further study the mean return interval $<\tau| \tau_0>$ after a cluster of $n$ intervals and the fluctuation $F(l)$ using detrended fluctuation analysis and find that long-term memory also exists in the volatility return intervals.
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PDF链接：
https://arxiv.org/pdf/0807.1818
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