Theory and applications of detrending-operation-based fractal-scaling analysis

摘要

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.