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

Abstract

We investigate how various coarse-graining 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 $\Delta$ 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 $\Delta <1$, while for $\Delta >1$ a crossover appears at small scales and moves to intermediate and large scales with increasing $\Delta$. For very rough coarse-graining ($\Delta >3$) 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 methods. 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.

19 pages, 13 figures

References in corpus (5)

• On the quantum, classical and total amount of correlations in a quantum state
• Comparison of detrending methods for fluctuation analysis
• Effect of nonlinear filters on detrended fluctuation analysis
• Effect of extreme data loss on long-range correlated and anti-correlated signals quantified by detrended fluctuation analysis
• Mutual Information as a Tool for Identifying Phase Transitions in Dynamical Complex Systems With Limited Data

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