Effect of the signal filtering on detrended fluctuation analysis

Detrended fluctuation analysis (DFA) is an effective method to accurately quantify long-term correlations embedded in a nonstationary time series. In this paper, we study the effect of signal filtering of a signal on the DFA method. The theoretical and simulated results show that the signal filtering will affect the range of scale in DFA. Moreover, this effect is different for fractal Gaussian noise series and fractal Brown movement series. Our study is meaningful for improving accuracy and efficiency of DFA method in theory and practice.