摘要翻译：
对于金融记录，在阈值$q$以上的挥发之间的回报间隔$\tau$的分布已经用一个缩放行为近似。为了探索尺度的准确性，从而理解划线的非线性机制，我们调查了标准普尔500指数组成的500只股票的日内数据集。我们发现，收益区间的累积分布与标度存在系统偏差。我们通过研究第m阶矩$\mu_m\equiv<(\tau/<\tau>)^m>^{1/m}$来支持这一发现，它们在平均间隔$<\tau>$时表现出一定的趋势。我们使用Schreiber方法生成代理记录，发现它们的累积分布几乎折叠成一条曲线，并且在$<\tau>$的大部分范围内矩几乎是常数。这些实质性的差异表明，原始波动率序列中的非线性相关解释了对单一标度律的偏离。我们还发现，由于记录的离散性和有限尺寸效应，原始记录和替代记录分别表现出短和长$<\tau>$的轻微趋势。为了尽可能地避免这些影响，我们研究了在$10<<\tau>\leq100$范围内的矩，并从拟合$\mu_m\sim<\tau>\\alpha$的幂律中发现指数$\alpha$在$\alpha\neq0$附近有一个狭窄的分布，对500只股票来说，这依赖于m。代理记录的$\alpha$分布非常窄，并且围绕$\alpha=0$。这表明，由于原始波动率的非线性相关性，收益率区间分布表现出多尺度行为。
---
英文标题：
《Indication of multiscaling in the volatility return intervals of stock
  markets》
---
作者：
Fengzhong Wang, Kazuko Yamasaki, Shlomo Havlin and H. Eugene Stanley
---
最新提交年份：
2007
---
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
--
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。
--

---
英文摘要：
  The distribution of the return intervals $\tau$ between volatilities above a threshold $q$ for financial records has been approximated by a scaling behavior. To explore how accurate is the scaling and therefore understand the underlined non-linear mechanism, we investigate intraday datasets of 500 stocks which consist of the Standard & Poor's 500 index. We show that the cumulative distribution of return intervals has systematic deviations from scaling. We support this finding by studying the m-th moment $\mu_m \equiv <(\tau/<\tau>)^m>^{1/m}$, which show a certain trend with the mean interval $<\tau>$. We generate surrogate records using the Schreiber method, and find that their cumulative distributions almost collapse to a single curve and moments are almost constant for most range of $<\tau>$. Those substantial differences suggest that non-linear correlations in the original volatility sequence account for the deviations from a single scaling law. We also find that the original and surrogate records exhibit slight tendencies for short and long $<\tau>$, due to the discreteness and finite size effects of the records respectively. To avoid as possible those effects for testing the multiscaling behavior, we investigate the moments in the range $10<<\tau>\leq100$, and find the exponent $\alpha$ from the power law fitting $\mu_m\sim<\tau>^\alpha$ has a narrow distribution around $\alpha\neq0$ which depend on m for the 500 stocks. The distribution of $\alpha$ for the surrogate records are very narrow and centered around $\alpha=0$. This suggests that the return interval distribution exhibit multiscaling behavior due to the non-linear correlations in the original volatility.
---
PDF链接：
https://arxiv.org/pdf/0707.4638