Effect of nonlinear correlations on the statistics of return intervals in multifractal data sets
Effect of nonlinear correlations on the statistics of return intervals in multifractal data sets
复制标题
DOI：
10.1103/physrevlett.99.240601
复制
发表时间：
2007-12-14
影响因子：
8.6
通讯作者：
Bunde, Armin
中科院分区：
文献类型：
--
作者：
Bogachev, Mikhail I.;Eichner, Jan F.;Bunde, Armin
在没有线性相关性的多重分形数据集中，研究了超过某一阈值的事件间返回间隔的统计量。我们发现，记录中的非线性相关性导致(I)回归区间的自相关函数的衰减，(Ii)条件回归周期的增加，以及(Iii)回归区间的概率密度函数的衰减。我们明确地表明，所有的观测量都依赖于阈值和系统大小，因此没有简单的标度观测。我们还证明，这种类型的行为可以在真实的经济记录中观察到，并可以用来显著改进风险估计。
We study the statistics of return intervals between events above a certain threshold in multifractal data sets without linear correlations. We find that nonlinear correlations in the record lead to a power-law (i) decay of the autocorrelation function of the return intervals, (ii) increase in the conditional return period, and (iii) decay in the probability density function of the return intervals. We show explicitly that all the observed quantities depend both on the threshold value and system size, and hence there is no simple scaling observed. We also demonstrate that this type of behavior can be observed in real economic records and can be used to improve considerably risk estimation.