Theory and applications of detrending-operation-based fractal-scaling analysis
Theory and applications of detrending-operation-based fractal-scaling analysis
复制标题
DOI：
10.1109/icnf.2017.7985951
复制
发表时间：
2017-06
期刊：
影响因子：
--
通讯作者：
K. Kiyono
中科院分区：
文献类型：
--
作者：
K. Kiyono
为了表征长期幂律相关性和分形标度行为，基于去趋势操作的分析方法，如去趋势波动分析（DFA）和去趋势移动平均分析（DMA），已被广泛使用。在这里，我们提出了一个总体框架，提供这样的尺度分析方法的数学基础。我们的算法可以提供由基于去趋势操作的分析估计的均方位移（MSD）统计量、自相关和二阶平稳过程的功率谱密度（PSD）之间的严格关系。作为代表性的例子，我们讨论了波动分析（FA），DFA和中心DMA的方法学特征。
To characterize long-range power-law correlations and fractal scaling behavior, detrending-operation-based analysis methods, such as the detrended fluctuation analysis (DFA) and the detrending moving average analysis (DMA), have become widely used. We here present a general framework to provide the mathematical foundations of such scaling analysis methods. Our ramework can provide the rigorous relation among mean-square-displacement (MSD) statistics estimated by the detrending-operation-based analysis, autocorrelation and power spectral density (PSD) for second-order stationary processes. As representative examples, we discuss the methodological features of the fluctuation analysis (FA), DFA and centered DMA.