Effects of coarse-graining on the scaling behavior of long-range correlated and anti-correlated signals.
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.
Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA ; College of Physics Science and Technology, Nanjing Normal University, Nanjing 210097, China.
Yinlin
Y
Xu
Harvard Medical School and Division of Sleep Medicine, Brigham & Women's Hospital, Boston, MA 02215, USA ; College of Geography and Biological Information, Nanjing University of Posts and Telecommunications, Nanjing 210003, China.
Qianli D Y
QD
Ma
Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA.
Daniel T
DT
Schmitt
Departamento de Física Aplicada II, Universidad de Málaga, 29071 Málaga, Spain.
Pedro
P
Bernaola-Galván
Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA ; Harvard Medical School and Division of Sleep Medicine, Brigham & Women's Hospital, Boston, MA 02215, USA ; Departamento de Física Aplicada II, Universidad de Málaga, 29071 Málaga, Spain.
Plamen Ch
PC
Ivanov
Coarse-graining; Detrended fluctuation analysis; Scaling behavior