Chaotic SVD method for 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 self-affine signals. 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 study, a smoothing algorithm based on the Chaotic Singular-Value Decomposition (CSVD) is proposed to minimize the effect of exponential trends and distortion in the log–log plots obtained by DFA techniques. The effectiveness of the technique is demonstrated on monofractal and multifractal data corrupted with exponential trends.