Chaotic SVD method for minimizing the effect of exponential trends in detrended fluctuation analysis |
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| Authors: | Pengjian Shang Aijing Lin |
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| Affiliation: | a Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, PR China
b Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA |
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| Abstract: | 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. |
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| Keywords: | Chaotic Singular-Value Decomposition (CSVD) Crossover Exponential trends Multifractal detrended fluctuation analysis (MF-DFA) Smoothing algorithm |
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