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摘要翻译：
高频采样的金融时间序列的对数收益概率分布是定量金融进一步发展的基础。在这封信中，我们给出了基于大量期货时间序列的实验结果。我们证明了$\nu\simeq3$的T-分布很好地描述了在$\delta t$小于1小时的时间尺度下考虑的几乎所有数据序列。对于$\delta t\ge8$hours，达到高斯状态。特别关注的是DAX和欧元期货。这似乎是一个相当普遍的结果，在一大组期货上保持稳健，但在任何数据集上都不是。从这个意义上说，这并不具有普遍性。本文描述了一种利用定义在一个返回序列上的阶乘矩的方法，并对时间尺度得到了类似的结果。让我们注意到，从基本观点来看，没有明确的理由为什么DAX和欧元期货在回报分布方面会呈现类似的行为。两者都是复杂的市场，许多内部和外部因素在每个瞬间相互作用，决定交易价格。对于变动平价指数（欧元）和股票指数(DAX)来说，这些因素肯定是不同的。因此，我们可以在这些市场的价格波动中找出普遍的统计特征，这是惊人的。这确实是微观结构分析的优势，以促进不同类型的市场的统一方法。最后，我们考察了收益率的幂律分布与编码为Hurst指数的数据的另一个标度行为之间的关系。我们得到了DAX的$H=0.54\PM 0.04美元和欧元期货的$H=0.51\PM 0.03美元。
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英文标题：
《Time Scales in Futures Markets and Applications》
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作者：
Laurent Schoeffel (CEA Saclay)
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最新提交年份：
2011
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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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英文摘要：
The probability distribution of log-returns for financial time series, sampled at high frequency, is the basis for any further developments in quantitative finance. In this letter, we present experimental results based on a large set of time series on futures. We show that the t-distribution with $\nu \simeq 3$ gives a nice description of almost all data series considered for a time scale $\Delta t$ below 1 hour. For $\Delta t \ge 8$ hours, the Gaussian regime is reached. A particular focus has been put on the DAX and Euro futures. This appears to be a quite general result that stays robust on a large set of futures, but not on any data sets. In this sense, this is not universal. A technique using factorial moments defined on a sequence of returns is described and similar results for time scales are obtained. Let us note that from a fundamental point of view, there is no clear reason why DAX and Euro futures should present similar behavior with respect to their return distributions. Both are complex markets where many internal and external factors interact at each instant to determine the transaction price. These factors are certainly different for an index on a change parity (Euro) and an index on stocks (DAX). Thus, this is striking that we can identify universal statistical features in price fluctuations of these markets. This is really the advantage of micro-structure analysis to prompt unified approaches of different kinds of markets. Finally, we examine the relation of power law distribution of returns with another scaling behavior of the data encoded into the Hurst exponent. We have obtained $H=0.54 \pm 0.04$ for DAX and $H=0.51 \pm 0.03$ for Euro futures.
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PDF链接：
https://arxiv.org/pdf/1110.1727
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