Analysis of clusters formed by the moving average of a long-range correlated time series
Analysis of clusters formed by the moving average of a long-range correlated time series
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DOI：
10.1103/physreve.69.026105
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发表时间：
2004-02-01
影响因子：
2.4
通讯作者：
Stanley, HE
中科院分区：
文献类型：
--
作者：
Carbone, A;Castelli, G;Stanley, HE
本文分析了随机函数C-n（i）等价toy（i）-y（n）（i），其中y（i）是长度为N-max的长程相关时间序列，y（n）（i）等价于（1/n）Sigma（k=0）（n-1）y（i-k）是窗口为n的移动平均。我们认为，C-n（i）生成一个自仿射簇C的长度为l，寿命为τ，面积为s的固定序列。长度和面积通过关系lsimilar totau（psi）l和ssimilar totau（s）（psi）与寿命相关，其中psil=1和psi（s）=1+H。我们还发现，l，tau和s是幂律分布，其指数取决于H：P（l）类似于tol（-alpha），P（tau）类似于totau（-beta），P（s）类似于tos（-gamma），其中alpha=beta=2-H和gamma=2/（1+H）。这些预测进行了测试，通过广泛的模拟系列所产生的中点位移算法的赫斯特指数H（范围从0.05到0.95）的长度高达N-max=2（21）和n高达2（13）。
We analyze the stochastic function C-n(i)equivalent toy(i)-y(n)(i), where y(i) is a long-range correlated time series of length N-max and y(n)(i)equivalent to(1/n)Sigma(k=0)(n-1)y(i-k) is the moving average with window n. We argue that C-n(i) generates a stationary sequence of self-affine clusters C with length l, lifetime tau, and area s. The length and the area are related to the lifetime by the relationships lsimilar totau(psi)l and ssimilar totau(s)(psi), where psil=1 and psi(s)=1+H. We also find that l, tau, and s are power law distributed with exponents depending on H: P(l)similar tol(-alpha), P(tau)similar totau(-beta), and P(s)similar tos(-gamma), with alpha=beta=2-H and gamma=2/(1+H). These predictions are tested by extensive simulations on series generated by the midpoint displacement algorithm of assigned Hurst exponent H (ranging from 0.05 to 0.95) of length up to N-max=2(21) and n up to 2(13).