摘要翻译：
我们研究了分散波动分析(DFA)的缩放机制--用于检测数据中长记忆的存在和时间序列的分形结构的最流行的方法。首先，研究了不相关数据在不同置信水平下DFA的标度范围随时间序列长度$L$和回归线系数$R^2$的变化。其次，对长记忆人工短序列进行了分析。在这两种情况下，缩放范围$\lambda$都是线性变化的--都是$L$和$R^2$。我们展示了如何将这种依赖关系推广到描述关系$\lambda=\lambda(L，R^2,H)$的简单统一模型，其中$H$($1/2\leqH\leq1$)代表长程自相关数据的Hurst指数。我们的研究结果对DFA技术的所有应用都是有用的，特别是对于瞬时（局部）DFA技术，在这种情况下，大量的短时间序列必须一次检查，而不可能分别对每个序列的标度范围进行初步检查。
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英文标题：
《On the scaling ranges of detrended fluctuation analysis for long-memory
  correlated short series of data》
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作者：
Dariusz Grech, Zygmunt Mazur
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最新提交年份：
2012
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分类信息：

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：Quantitative Finance        数量金融学
二级分类：General Finance        一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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英文摘要：
  We examine the scaling regime for the detrended fluctuation analysis (DFA) - the most popular method used to detect the presence of long memory in data and the fractal structure of time series. First, the scaling range for DFA is studied for uncorrelated data as a function of length $L$ of time series and regression line coefficient $R^2$ at various confidence levels. Next, an analysis of artificial short series with long memory is performed. In both cases the scaling range $\lambda$ is found to change linearly -- both with $L$ and $R^2$. We show how this dependence can be generalized to a simple unified model describing the relation $\lambda=\lambda(L, R^2, H)$ where $H$ ($1/2\leq H \leq 1$) stands for the Hurst exponent of long range autocorrelated data. Our findings should be useful in all applications of DFA technique, particularly for instantaneous (local) DFA where enormous number of short time series has to be examined at once, without possibility for preliminary check of the scaling range of each series separately.
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PDF链接：
https://arxiv.org/pdf/1206.1007