Comparison of applications of different filter methods for de-noising detrended fluctuation analysis

We studied the effects of continuous noises and random spikes on detrended fluctuation analysis, and found that the noises lead to the appearance of crossovers in the double logarithm curves when the linear fitting scale was less than a characteristic scale s×. To solve this problem, we use three kinds of filter methods, multi-stage Vondrak filter, N-point weighted moving average filter and fast Fourier filter, to filter high frequency from the analyzed time series. The results indicate that the evolution trend and intensity of high frequency series by multi-stage Vondrak filter is almost identical to those of real noises. Further investigation showed that multi-stage Vondrak filter can eliminate the phenomenon of crossover, and the DFA results of lowpass filtering time series are less dependent on the threshold of the filter periods. To some extent, N-points weighted moving average filter can partly eliminate the effect of noises on DFA, but can not completely eliminate the phenomenon of crossover caused by noises. Fast Fourier filter can almost totally eliminate the effect of noises on DFA when the period of filter adopts an appropriate value, but the filtering results have a stronger dependence on the period of filter, so it is difficult to select the period of filter in practical application. Therefore, comparatively speaking, multi-stage Vondrak filter is an effective measure to alleviate the effects of noises on the DFA results.