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Effects of coarse-graining on the scaling behavior of long-range correlated and anti-correlated signals

Author

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  • Xu, Yinlin
  • Ma, Qianli D.Y.
  • Schmitt, Daniel T.
  • Bernaola-Galván, Pedro
  • Ivanov, Plamen Ch.

Abstract

We investigate how various coarse-graining (signal quantization) methods affect the scaling properties of long-range power-law correlated and anti-correlated signals, quantified by the detrended fluctuation analysis. Specifically, for coarse-graining in the magnitude of a signal, we consider (i) the Floor, (ii) the Symmetry and (iii) the Centro-Symmetry coarse-graining methods. We find that for anti-correlated signals coarse-graining in the magnitude leads to a crossover to random behavior at large scales, and that with increasing the width of the coarse-graining partition interval Δ, this crossover moves to intermediate and small scales. In contrast, the scaling of positively correlated signals is less affected by the coarse-graining, with no observable changes when Δ<1, while for Δ>1 a crossover appears at small scales and moves to intermediate and large scales with increasing Δ. For very rough coarse-graining (Δ>3) based on the Floor and Symmetry methods, the position of the crossover stabilizes, in contrast to the Centro-Symmetry method where the crossover continuously moves across scales and leads to a random behavior at all scales; thus indicating a much stronger effect of the Centro-Symmetry compared to the Floor and the Symmetry method. For coarse-graining in time, where data points are averaged in non-overlapping time windows, we find that the scaling for both anti-correlated and positively correlated signals is practically preserved. The results of our simulations are useful for the correct interpretation of the correlation and scaling properties of symbolic sequences.

Suggested Citation

  • Xu, Yinlin & Ma, Qianli D.Y. & Schmitt, Daniel T. & Bernaola-Galván, Pedro & Ivanov, Plamen Ch., 2011. "Effects of coarse-graining on the scaling behavior of long-range correlated and anti-correlated signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4057-4072.
  • Handle: RePEc:eee:phsmap:v:390:y:2011:i:23:p:4057-4072
    DOI: 10.1016/j.physa.2011.05.015
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    Cited by:

    1. Zhang, Yin & Li, Jin & Wang, Jun, 2017. "Exploring stability of entropy analysis for signal with different trends," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 60-67.
    2. Li, Jin & Chen, Chen & Yao, Qin & Zhang, Peng & Wang, Jun & Hu, Jing & Feng, Feilong, 2018. "The effect of circadian rhythm on the correlation and multifractality of heart rate signals during exercise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 1207-1213.
    3. Yao, Wenpo & Zhang, Yuping & Wang, Jun, 2018. "Quantitative analysis in nonlinear complexity detection of meditative heartbeats," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 1060-1068.

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