Modeling correlated bursts by the bursty-get-burstier mechanism

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.

7 pages, 5 figures

References in corpus (3)

• Small But Slow World: How Network Topology and Burstiness Slow Down Spreading
• Universality in solar flare and earthquake occurrence
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Cited by in corpus (6)

• Analytically solvable autocorrelation function for weakly correlated interevent times
• Temperature-dependent criticality in random 2D Ising models
• Burst-tree structure and higher-order temporal correlations
• Temporal scaling theory for bursty time series with clusters of arbitrarily many events
• Analysis of the autocorrelation function for time series with higher-order temporal correlations: An exponential case
• Hierarchical organization of bursty trains in event sequences