Chen Zhi, Ivanov Plamen Ch, Hu Kun, Stanley H Eugene
Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Apr;65(4 Pt 1):041107. doi: 10.1103/PhysRevE.65.041107. Epub 2002 Apr 8.
Detrended fluctuation analysis (DFA) is a scaling analysis method used to quantify long-range power-law correlations in signals. Many physical and biological signals are "noisy," heterogeneous, and exhibit different types of nonstationarities, which can affect the correlation properties of these signals. We systematically study the effects of three types of nonstationarities often encountered in real data. Specifically, we consider nonstationary sequences formed in three ways: (i) stitching together segments of data obtained from discontinuous experimental recordings, or removing some noisy and unreliable parts from continuous recordings and stitching together the remaining parts-a "cutting" procedure commonly used in preparing data prior to signal analysis; (ii) adding to a signal with known correlations a tunable concentration of random outliers or spikes with different amplitudes; and (iii) generating a signal comprised of segments with different properties-e.g., different standard deviations or different correlation exponents. We compare the difference between the scaling results obtained for stationary correlated signals and correlated signals with these three types of nonstationarities. We find that introducing nonstationarities to stationary correlated signals leads to the appearance of crossovers in the scaling behavior and we study how the characteristics of these crossovers depend on (a) the fraction and size of the parts cut out from the signal, (b) the concentration of spikes and their amplitudes (c) the proportion between segments with different standard deviations or different correlations and (d) the correlation properties of the stationary signal. We show how to develop strategies for preprocessing "raw" data prior to analysis, which will minimize the effects of nonstationarities on the scaling properties of the data, and how to interpret the results of DFA for complex signals with different local characteristics.
去趋势波动分析（DFA）是一种用于量化信号中长程幂律相关性的标度分析方法。许多物理和生物信号是“有噪声的”、异质的，并且表现出不同类型的非平稳性，这可能会影响这些信号的相关特性。我们系统地研究了实际数据中经常遇到的三种非平稳性的影响。具体来说，我们考虑以三种方式形成的非平稳序列：（i）将从不连续实验记录中获得的数据段拼接在一起，或者从连续记录中去除一些噪声大且不可靠的部分，然后将其余部分拼接在一起——这是信号分析前数据预处理中常用的“切割”过程；（ii）向具有已知相关性的信号中添加可调浓度的不同幅度的随机异常值或尖峰；（iii）生成一个由具有不同特性（例如，不同标准差或不同相关指数）的段组成的信号。我们比较了平稳相关信号和具有这三种非平稳性的相关信号的标度结果之间的差异。我们发现，将非平稳性引入平稳相关信号会导致标度行为中出现交叉，并且我们研究了这些交叉的特征如何取决于（a）从信号中切除的部分的比例和大小，（b）尖峰的浓度及其幅度，（c）具有不同标准差或不同相关性的段之间的比例，以及（d）平稳信号的相关特性。我们展示了如何在分析之前制定“原始”数据的预处理策略，这将最小化非平稳性对数据标度特性的影响，以及如何解释具有不同局部特征的复杂信号的DFA结果。
