Asia Pacific Center for Theoretical Physics, Pohang 37673, Republic of Korea; Department of Physics, Pohang University of Science and Technology, Pohang 37673, Republic of Korea; and Department of Computer Science, Aalto University, Espoo FI-00076, Finland.
Phys Rev E. 2017 Dec;96(6-1):062131. doi: 10.1103/PhysRevE.96.062131. Epub 2017 Dec 18.
Temporal correlations of time series or event sequences in natural and social phenomena have been characterized by power-law decaying autocorrelation functions with decaying exponent γ. Such temporal correlations can be understood in terms of power-law distributed interevent times with exponent α and/or correlations between interevent times. The latter, often called correlated bursts, has recently been studied by measuring power-law distributed bursty trains with exponent β. A scaling relation between α and γ has been established for the uncorrelated interevent times, while little is known about the effects of correlated interevent times on temporal correlations. In order to study these effects, we devise the bursty-get-burstier model for correlated bursts, by which one can tune the degree of correlations between interevent times, while keeping the same interevent time distribution. We numerically find that sufficiently strong correlations between interevent times could violate the scaling relation between α and γ for the uncorrelated case. A nontrivial dependence of γ on β is also found for some range of α. The implication of our results is discussed in terms of the hierarchical organization of bursty trains at various time scales.
自然和社会现象中时间序列或事件序列的时间相关性，其自相关函数具有随指数γ衰减的幂律衰减。这种时间相关性可以用具有指数α和/或事件之间相关性的幂律分布的事件间时间来理解。后者通常称为相关突发，最近通过测量具有指数β的幂律分布突发列车来研究。已经建立了无关联事件间时间的α和γ之间的标度关系，而对于相关事件间时间对时间相关性的影响知之甚少。为了研究这些影响，我们设计了用于相关突发的突发变得更突发的模型，通过该模型，可以在保持相同的事件间时间分布的情况下调整事件间时间之间的相关性程度。我们通过数值发现，事件间时间之间的相关性足够强，可能会违反无相关情况下α和γ之间的标度关系。还发现，对于某些α范围，γ对β存在非平凡的依赖性。我们的结果的含义是根据各种时间尺度上突发列车的层次组织来讨论的。
