Burst-tree decomposition of time series reveals the structure of temporal correlations

Abstract

Comprehensive characterization of non-Poissonian, bursty temporal patterns observed in various natural and social processes is crucial to understand the underlying mechanisms behind such temporal patterns. Among them bursty event sequences have been studied mostly in terms of interevent times (IETs), while the higher-order correlation structure between IETs has gained very little attention due to the lack of a proper characterization method. In this paper we propose a method of decomposing an event sequence into a set of IETs and a burst tree, which exactly captures the structure of temporal correlations that is entirely missing in the analysis of IET distributions. We apply the burst-tree decomposition method to various datasets and analyze the structure of the revealed burst trees. In particular, we observe that event sequences show similar burst-tree structure, such as heavy-tailed burst size distributions, despite of very different IET distributions. The burst trees allow us to directly characterize the preferential and assortative mixing structure of bursts responsible for the higher-order temporal correlations. We also show how to use the decomposition method for the systematic investigation of such higher-order correlations captured by the burst trees in the framework of randomized reference models. Finally, we devise a simple kernel-based model for generating event sequences showing appropriate higher-order temporal correlations. Our method is a tool to make the otherwise overwhelming analysis of higher-order correlations in bursty time series tractable by turning it into the analysis of a tree structure.

10 pages, 4 figures

References in corpus (10)

• From time series to complex networks: the visibility graph
• Small But Slow World: How Network Topology and Burstiness Slow Down Spreading
• A Poissonian explanation for heavy-tails in e-mail communication
• On Universality in Human Correspondence Activity
• Bursty Human Dynamics
• Universality in solar flare and earthquake occurrence
• Impact of memory on human dynamics
• Correlated bursts in temporal networks slow down spreading
• Modeling correlated bursts by the bursty-get-burstier mechanism
• Hierarchical burst model for complex bursty dynamics

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• Copula-based analysis of the autocorrelation function for simple temporal networks
• Analysis of the autocorrelation function for time series with higher-order temporal correlations: An exponential case
• Hierarchical organization of bursty trains in event sequences
• Maximum likelihood estimation of burst-merging kernels for bursty time series