Modeling correlated bursts by the bursty-get-burstier mechanism

TL;DR

This paper introduces the bursty-get-burstier model to study how correlations between interevent times influence temporal correlations in event sequences, revealing violations of known scaling relations and complex dependencies.

Contribution

The paper develops a new model that allows tuning correlations between interevent times while maintaining the same distribution, advancing understanding of temporal correlations in bursty event sequences.

Findings

Strong correlations can violate the uncorrelated scaling relation.

Dependence of autocorrelation exponent on burst train exponent is complex.

Hierarchical organization of bursty trains affects temporal correlations.

Abstract

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 $\gamma$. Such temporal correlations can be understood in terms of power-law distributed interevent times with exponent $\alpha$, 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 $\beta$. A scaling relation between $\alpha$ and $\gamma$ 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 $\alpha$ and $\gamma$ for the uncorrelated case. A non-trivial dependence of $\gamma$ on $\beta$ is also found for some range of $\alpha$. The implication of our results is discussed in terms of the hierarchical organization of bursty trains at various timescales.