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摘要翻译：
离散涨落分析(DFA)是研究非平稳时间序列幂律长期相关性的一种简单而有效的方法，它需要通过离散步骤来获得不同时间尺度上的局部涨落。提出通过经验模态分解(EMD)来确定局部趋势，并通过去除基于EMD的局部趋势来进行去中心化操作，从而给出了一种基于EMD的DFA方法。同样，我们还提出了一种改进的多重分形DFA算法，称为基于EMD的MFDFA。通过基于分数布朗运动和乘法级联过程的大量数值实验，对基于EMD的DFA和MFDFA方法的性能进行了评估。我们发现，当时间序列存在强反相关时，基于EMD的DFA方法在Hurst指数的确定上优于经典的DFA方法；当衰减波动的矩阶为正数时，基于EMD的MFDFA方法优于传统的MFDFA方法。我们将基于EMD的MFDFA应用于上证综合指数的一分钟数据，证实了多重分形的存在。
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英文标题：
《Modified detrended fluctuation analysis based on empirical mode
decomposition》
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作者：
Xi-Yuan Qian, Wei-Xing Zhou, Gao-Feng Gu (ECUST)
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最新提交年份：
2009
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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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：
Detrended fluctuation analysis (DFA) is a simple but very efficient method for investigating the power-law long-term correlations of non-stationary time series, in which a detrending step is necessary to obtain the local fluctuations at different timescales. We propose to determine the local trends through empirical mode decomposition (EMD) and perform the detrending operation by removing the EMD-based local trends, which gives an EMD-based DFA method. Similarly, we also propose a modified multifractal DFA algorithm, called an EMD-based MFDFA. The performance of the EMD-based DFA and MFDFA methods is assessed with extensive numerical experiments based on fractional Brownian motion and multiplicative cascading process. We find that the EMD-based DFA method performs better than the classic DFA method in the determination of the Hurst index when the time series is strongly anticorrelated and the EMD-based MFDFA method outperforms the traditional MFDFA method when the moment order $q$ of the detrended fluctuations is positive. We apply the EMD-based MFDFA to the one-minute data of Shanghai Stock Exchange Composite index, and the presence of multifractality is confirmed.
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PDF链接：
https://arxiv.org/pdf/0907.3284
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