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首页> 外文期刊>Physica, A. Statistical mechanics and its applications >Effects of coarse-graining on the scaling behavior of long-range correlated and anti-correlated signals
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Effects of coarse-graining on the scaling behavior of long-range correlated and anti-correlated signals

机译：粗粒度对远程相关和反相关信号的缩放行为的影响

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摘要

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.
机译：我们研究了各种粗粒度（信号量化）方法如何影响远程幂律相关信号和反相关信号的缩放特性，并通过去趋势波动分析对其进行了量化。具体来说，对于信号幅度的粗粒度，我们考虑（i）底限，（ii）对称性和（iii）中心对称粗粒度方法。我们发现，对于反相关信号，幅度上的粗粒度导致大尺度上的随机行为的交叉，并且随着粗粒度划分间隔Δ宽度的增加，这种交叉移动到中小尺度。相反，正相关信号的缩放受粗粒度的影响较小，当Δ<1时没有可观察到的变化，而对于Δ> 1，分频出现在小范围，并随着Δ的增加而移至中大范围。对于基于地板和对称方法的非常粗糙的粗粒度（Δ> 3），与中心对称方法相反，分频器的位置稳定，与之不同的是，分频器在各个标度上连续移动并导致在所有标度上具有随机行为;因此，与Floor和Symmetry方法相比，Centro-Symmetry的效果要强得多。对于时间上的粗粒度（在非重叠时间窗口中对数据点进行平均），我们发现实际上保留了反相关和正相关信号的缩放比例。我们的仿真结果对于正确解释符号序列的相关性和缩放属性很有用。

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