1 research outputs found
Effects of coarse-graining on the scaling behavior of long-range correlated and anti-correlated signals
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 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 a crossover appears at small
scales and moves to intermediate and large scales with increasing . For
very rough coarse-graining () 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.Comment: 19 pages, 13 figure