摘要翻译：
我们系统地研究了外汇市场高频收益的各种统计特征。本研究基于形成两个三角形的六种汇率：欧元-英镑-美元和英镑-瑞郎-日元。结果表明，所有对的汇率收益率波动都可以用q-高斯的非广泛统计量来描述。对于不同的汇率，Q参数的非扩展性值在数量上存在一些小的变化，这可能与给定的汇率在世界货币贸易中的重要性有关。然而，时间相关性组织了收益率序列，使得它们发展了所有汇率的多重分形特征，其奇异性谱f(alpha)的对称程度不同。对于英镑/美元，识别出最对称的频谱。我们还构造了三角形剩余收益的时间序列，发现它们的波动分布与小波动相比发展出不成比例的重尾，这排除了用q-高斯描述的可能性。这些剩余收益的多重分形特征揭示了负奇异指数甚至负奇异谱等异常性质。这种反常的多重分形测度到目前为止在文献中已经考虑到与扩散、有限聚集和湍流有关的问题。我们发现，在短时间尺度上的市场非效率会导致在长时间尺度上的Epps效应的发生。虽然货币市场的流动性比股票市场大得多，交易频率也大得多，但相关关系的建立需要几个小时的时间，这与股票市场上观察到的情况没有太大差异。这可能表明，交易的非同步性并不是所观察到的效应的唯一来源。
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英文标题：
《The foreign exchange market: return distributions, multifractality,
  anomalous multifractality and Epps effect》
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作者：
Stanislaw Drozdz, Jaroslaw Kwapien, Pawel Oswiecimka, Rafal Rak
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最新提交年份：
2010
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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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英文摘要：
  We present a systematic study of various statistical characteristics of high-frequency returns from the foreign exchange market. This study is based on six exchange rates forming two triangles: EUR-GBP-USD and GBP-CHF-JPY. It is shown that the exchange rate return fluctuations for all the pairs considered are well described by the nonextensive statistics in terms of q-Gaussians. There exist some small quantitative variations in the nonextensivity q-parameter values for different exchange rates and this can be related to the importance of a given exchange rate in the world's currency trade. Temporal correlations organize the series of returns such that they develop the multifractal characteristics for all the exchange rates with a varying degree of symmetry of the singularity spectrum f(alpha) however. The most symmetric spectrum is identified for the GBP/USD. We also form time series of triangular residual returns and find that the distributions of their fluctuations develop disproportionately heavier tails as compared to small fluctuations which excludes description in terms of q-Gaussians. The multifractal characteristics for these residual returns reveal such anomalous properties like negative singularity exponents and even negative singularity spectra. Such anomalous multifractal measures have so far been considered in the literature in connection with the diffusion limited aggregation and with turbulence. We find that market inefficiency on short time scales leads to the occurrence of the Epps effect on much longer time scales. Although the currency market is much more liquid than the stock markets and it has much larger transaction frequency, the building-up of correlations takes up to several hours - time that does not differ much from what is observed in the stock markets. This may suggest that non-synchronicity of transactions is not the unique source of the observed effect.
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PDF链接：
https://arxiv.org/pdf/1011.2385