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Detrended fluctuation analysis based on best-fit polynomial

Detrended fluctuation analysis (DFA) can quantify long-range correlation (LRC) and fractal scaling behavior of signal. We compared the results of variant DFA methods by varying the order of the polynomial and found that the order of 6 was relatively better than the others when both the accuracy and computational cost were taken into account. An alternative DFA method is proposed to quantify the LRC exponent by using best-fit polynomial algorithm in each segment instead of the polynomial of the same order in all of segments. In this study, the best-fit polynomial algorithm with the maximum order of 6 is used to fit the local trend in each segment to detrend the trend of a time series, and then the revised DFA is used to quantify the LRC in the time series. A series of numerical studies demonstrate that the best-fit DFA performs better than regular DFA, especially for the time series with scaling exponent smaller than 0.5. This may be attributed to the improvement of the fitted trend at the end of each segment. The estimation results of variant DFA methods reach stable when the time series length is greater than 1,000.