Higher-Order Correlations in Bursty Temporal Patterns

Temporal inhomogeneities in event sequences of natural and social phenomena have been characterized in terms of interevent times and correlations between interevent times. The inhomogeneities of interevent times have been extensively studied, while the correlations between interevent times, correlated bursts (CB), are far from being fully understood. Firstly, we numerically show that the strong CB, depicted by power-law burst size distributions, violates the well-established scaling relation between the power-law decaying autocorrelation function and the power-law interevent time distribution (PRE 2017). Next, for understanding empirical data sets for human activities showing power-law burst size distributions but negligible memory coefficient, we derive an analytic form of the memory coefficient between consecutive interevent times as a function of parameters describing interevent time and burst size statistics, to conclude that the memory coefficient might have some limits in quantifying CB (PRE 2018). Finally, in order to completely characterize the event sequence, we develop a detection method of the hierarchical burst structure by exactly mapping the event sequence onto a rooted tree, implying no loss of information on the original event sequence (in preparation).