Effect of trends on detrended fluctuation analysis
Effect of trends on detrended fluctuation analysis
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DOI：
10.1103/physreve.64.011114
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发表时间：
2001-07-01
影响因子：
2.4
通讯作者：
Stanley, HE
中科院分区：
文献类型：
--
作者：
Hu, K;Ivanov, PC;Stanley, HE
去趋势波动分析 (DFA) 是一种标度分析方法，用于估计噪声信号中的长程幂律相关指数。实际系统中许多噪声信号显示趋势，使得从DFA方法获得的缩放结果变得难以分析。我们系统地研究了三种趋势的影响——线性趋势、周期性趋势和幂律趋势，并提供了这些趋势在实际数据中可能出现的示例。我们比较了人工生成的相关噪声和具有趋势的相关噪声的缩放结果之间的差异，并研究趋势如何导致缩放行为中出现交叉。我们发现交叉是由噪声的缩放和趋势的“表观”缩放之间的竞争造成的。我们研究这些交叉的特征如何取决于（i）线性趋势的斜率：（ii）周期性趋势的幅度和周期； (iii) 幂律趋势的幅度和功率，以及 (iv) 噪声的长度和相关特性。令人惊讶的是，我们发现噪声信号与趋势的缩放中的交叉也遵循缩放定律，即交叉位置对趋势参数的长程幂律依赖性。我们证明，具有趋势的噪声的 DFA 结果可以通过将 DFA 的单独结果叠加在噪声和趋势上来精确确定。假设噪声和趋势不相关。如果不遵循该叠加规则，则表明噪声和叠加趋势不是独立的，因此去除趋势可能会导致噪声的相关属性发生变化。此外，我们还展示了如何适当地使用 DFA 来最小化趋势的影响，如何识别交叉是否确实表明从一种类型到另一种类型的潜在相关性的转变，或者交叉是否是由于噪声动态属性没有任何转变的趋势所致。
Detrended fluctuation analysis (DFA) is a scaling analysis method used to estimate long-range power-law correlation exponents in noisy signals. Many noisy signals in real systems display trends, so that the scaling results obtained from the DFA method become difficult to analyze. We systematically study the effects of three types of trends - linear, periodic, and power-law trends, and offer examples where these trends are likely to occur in real data. We compare the difference between the scaling results for artificially generated correlated noise and correlated noise with a trend, and study how trends lead to the appearance of crossovers in the scaling behavior. We find that crossovers result from the competition between the scaling of the noise and the "apparent" scaling of the trend. We study how the characteristics of these crossovers depend on (i) the slope of the linear trend: (ii) the amplitude and period of the periodic trend; (iii) the amplitude and power of the power-law trend, and (iv) the length as well as the correlation properties of the noise. Surprisingly, we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws-i.e., long-range power-law dependence of the position of the crossover on the parameters of the trends. We show that the DFA result of noise with a trend can be exactly determined by the superposition of the separate results of the DFA on the noise and on the trend. assuming that the noise and the trend are not correlated. If this superposition rule is not followed, this is an indication that the noise and the superposed trend are not independent, so that removing the trend could lead to changes in the correlation properties of the noise. In addition, we show how to use DFA appropriately to minimize the effects of trends, how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation, or if the crossover is due to a trend without any transition in the dynamical properties of the noise.