A Model of Coarse-Graining Effect on DFA

Detrended fluctuation analysis (DFA) is a scaling method used to estimate long-range power-law correlation exponents in noisy signals. Data acquisition is an inherent part of the method. Continuous signals are converted into discretized, digital signals when the signals are sampled and then quantized, and the digital signals shall be referred to as coarse-grained results. In addition, coarse-graining is also a useful means to get robust information of a dynamical system by mapping original signals into symbol sequences. Therefore, it is important to learn how coarse-graining affects the results of DFA for signals. In this paper, we study the effects of coarse-graining on DFA for noisy signals with three types of correlation properties, i.e. anti-correlated, long-range correlated and uncorrelated signals. The result shows that the effects of coarse-graining on DFA are closely related to the correlation properties of signals. To understand the scaling behavior of coarse-grained signals, we discuss the properties of difference signals caused by coarse-graining procedure, and then describe a coarse-grained signal as an additive white noise signal with the original signal. Finally, we build a model for accurately simulating the scaling of coarse-grained signals by means of superposition rule of rms fluctuation function.