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Comprehensive characterization of non-Poissonian, bursty temporal patternsobserved in various natural and social processes is crucial to understand theunderlying mechanisms behind such temporal patterns. Among them bursty eventsequences have been studied mostly in terms of interevent times (IETs), whilethe higher-order correlation structure between IETs has gained very littleattention due to the lack of a proper characterization method. In this paper wepropose a method of decomposing an event sequence into a set of IETs and aburst tree, which exactly captures the structure of temporal correlations thatis entirely missing in the analysis of IET distributions. We apply theburst-tree decomposition method to various datasets and analyze the structureof the revealed burst trees. In particular, we observe that event sequencesshow similar burst-tree structure, such as heavy-tailed burst sizedistributions, despite of very different IET distributions. The burst treesallow us to directly characterize the preferential and assortative mixingstructure of bursts responsible for the higher-order temporal correlations. Wealso show how to use the decomposition method for the systematic investigationof such higher-order correlations captured by the burst trees in the frameworkof randomized reference models. Finally, we devise a simple kernel-based modelfor generating event sequences showing appropriate higher-order temporalcorrelations. Our method is a tool to make the otherwise overwhelming analysisof higher-order correlations in bursty time series tractable by turning it intothe analysis of a tree structure.

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