Minimizing the effect of exponential trends in detrended fluctuation analysis

The detrended fluctuation analysis (DFA) and its extensions (MF-DFA) have been used extensively to determine possible long-range correlations in time series. However, recent studies have reported the susceptibility of DFA to trends which give rise to spurious crossovers and prevent reliable estimation of the scaling exponents. In this report, a smoothing algorithm based on the discrete laplace transform (DFT) is proposed to minimize the effect of exponential trends and distortion in the log–log plots obtained by MF-DFA techniques. The effectiveness of the technique is demonstrated on monofractal and multifractal data corrupted with exponential trends.