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Minimizing the effect of trends on detrended fluctuation analysis of long-range correlated noise

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  • Nagarajan, Radhakrishnan
  • Kavasseri, Rajesh G.

Abstract

Detrended fluctuation analysis (DFA) has been proposed as a robust technique to determine possible long-range correlations in power-law processes (Phys. Rev. E 49 (1994) 1685–1989). However, recent studies have reported the susceptibility of DFA to trends [(Phys. Rev. E 64 (2001) 011114–011133)] which give rise to spurious crossovers and prevent reliable estimation of the scaling exponents. Inspired by these reports, we propose a technique based on singular-value decomposition (SVD) of the trajectory matrix to minimize the effect of linear, power-law, periodic and also quasi-periodic trends superimposed on long-range correlated power-law noise. The effectiveness of the technique is demonstrated on publicly available data sets [(Phys. Rev. E 64 (2001) 011114–011133)].

Suggested Citation

  • Nagarajan, Radhakrishnan & Kavasseri, Rajesh G., 2005. "Minimizing the effect of trends on detrended fluctuation analysis of long-range correlated noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 182-198.
    • Handle: RePEc:eee:phsmap:v:354:y:2005:i:c:p:182-198
    DOI: 10.1016/j.physa.2005.01.041
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    3. Leonarduzzi, R. & Wendt, H. & Abry, P. & Jaffard, S. & Melot, C. & Roux, S.G. & Torres, M.E., 2016. "p-exponent and p-leaders, Part II: Multifractal analysis. Relations to detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 319-339.
    4. Nagarajan, Radhakrishnan, 2006. "Reliable scaling exponent estimation of long-range correlated noise in the presence of random spikes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 1-17.
    5. Zhao, Xiaojun & Shang, Pengjian & Zhao, Chuang & Wang, Jing & Tao, Rui, 2012. "Minimizing the trend effect on detrended cross-correlation analysis with empirical mode decomposition," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 166-173.
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    8. Michalski, Sebastian, 2008. "Blocks adjustment—reduction of bias and variance of detrended fluctuation analysis using Monte Carlo simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 217-242.

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