A Model of Coarse-Graining Effect on DFA

Abstract —Detrended Fluctuation Analysis (DFA) is a scalingmethod used to estimate long-range power-law correlation expo-nents in noisy signals. Data acquisition is an inherent part ofthe 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-grainedresults. In addition, coarse-graining is also a useful means to getrobust information of a dynamical system by mapping originalsignals into symbol sequences. Therefore, it is important tolearn how coarse-graining affects the results of DFA for signals.In this paper, we study the effects of coarse-graining on DFAfor 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 DFAare closely related to the correlation properties of signals. Tounderstand the scaling behavior of coarse-grained signals, wediscuss the properties of difference signals caused by coarse-graining procedure, and then describe a coarse-grained signal asan 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 fluctuationfunction.

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