摘要翻译：
平稳增量的条件，而不是标度，决定了长时间对自相关。当增量非平稳时，不正确的平稳增量假设会产生虚假的程式化事实、肥尾和Hurst指数H_s=1/2，就像在外汇市场上一样。这种非平稳性是由噪声交易者行为的系统不均匀性引起的。在数学上，使用带有“滑动窗口”的日志增量会产生虚假的结果。我们解释了为什么一个难以打败的市场需要鞅动力学，而具有非线性方差的鞅产生非平稳增量。这种非平稳性直接表现在欧元/美元外汇数据上。我们观察到，利用滑动窗口技术在时间序列上产生的Hurst指数H_s与Mandelbrot的Joseph指数具有相同的作用。最后，Mandelbrot最初假设棉花收益的“不良行为”二阶矩是由于肥尾，但这种不收敛的行为反而是非平稳增量的直接证据。总之，作为经济物理学和金融经济学基础的标度和肥尾的证据既不是由外汇市场提供的，也不是由棉花价格数据提供的。
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英文标题：
《Martingales, the Efficient Market Hypothesis, and Spurious Stylized
  Facts》
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作者：
Joseph L. McCauley, Kevin E. Bassler, and Gemunu H. Gunaratne
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最新提交年份：
2007
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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 condition for stationary increments, not scaling, detemines long time pair autocorrelations. An incorrect assumption of stationary increments generates spurious stylized facts, fat tails and a Hurst exponent H_s=1/2, when the increments are nonstationary, as they are in FX markets. The nonstationarity arises from systematic uneveness in noise traders' behavior. Spurious results arise mathematically from using a log increment with a 'sliding window'. We explain why a hard to beat market demands martingale dynamics , and martingales with nonlinear variance generate nonstationary increments. The nonstationarity is exhibited directly for Euro/Dollar FX data. We observe that the Hurst exponent H_s generated by the using the sliding window technique on a time series plays the same role as does Mandelbrot's Joseph exponent. Finally, Mandelbrot originally assumed that the 'badly behaved' second moment of cotton returns is due to fat tails, but that nonconvergent behavior is instead direct evidence for nonstationary increments. Summarizing, the evidence for scaling and fat tails as the basis for econophysics and financial economics is provided neither by FX markets nor by cotton price data.
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PDF链接：
https://arxiv.org/pdf/0710.2583