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.

arXiv comment7 pages, 5 figures

References in corpus (20)

• The origin of bursts and heavy tails in human dynamics
• Detecting Long-range Correlations with Detrended Fluctuation Analysis
• Small But Slow World: How Network Topology and Burstiness Slow Down Spreading
• Long-Term Clustering, Scaling, and Universality in the Temporal Occurrence of Earthquakes
• Impact of non-Poisson activity patterns on spreading processes
• The dynamical strength of social ties in information spreading
• Scaling laws of human interaction activity
• Common Scaling Patterns in Intertrade Times of U. S. Stocks
• Diffusion on networked systems is a question of time or structure
• Universality in solar flare and earthquake occurrence
• Communication activity in a social network: relation between long-term correlations and inter-event clustering
• Correlated dynamics in egocentric communication networks
• Measuring burstiness for finite event sequences
• Analytically Solvable Model of Spreading Dynamics with Non-Poissonian Processes
• Correlated bursts and the role of memory range
• Modelling bursty time series
• Violation of the scaling relation and non-Markovian nature of earthquake aftershocks
• Two-state Markov-chain Poisson nature of individual cellphone call statistics
• Contextual analysis framework for bursty dynamics
• Uncovering the evolution of non-stationary stochastic variables: the example of asset volume-price fluctuations

Cited by in corpus (12)

• Correlated bursts in temporal networks slow down spreading
• Copula-based algorithm for generating bursty time series
• Hierarchical burst model for complex bursty dynamics
• Burst-tree decomposition of time series reveals the structure of temporal correlations
• Analytically solvable autocorrelation function for weakly correlated interevent times
• Limits of memory coefficient in measuring correlated bursts
• Temperature-dependent criticality in random 2D Ising models
• Individual-driven versus interaction-driven burstiness in human dynamics: The case of Wikipedia edit history
• Temporal scaling theory for bursty time series with clusters of arbitrarily many events
• Burst-tree structure and higher-order temporal correlations
• Analysis of the autocorrelation function for time series with higher-order temporal correlations: An exponential case
• Hierarchical organization of bursty trains in event sequences