Correlated bursts and the role of memory range

TL;DR

This paper introduces a simple self-exciting point process model with variable memory range to explain correlated bursts in natural and social phenomena, highlighting how different memory effects influence burst patterns.

Contribution

The study proposes a novel model incorporating variable memory range and memory loss mechanisms to better understand correlated bursts in temporal processes.

Findings

Excessive memory can lead to Poissonian (uncorrelated) processes.

Intermediate memory ranges produce correlated bursts similar to empirical data.

Memory effects significantly influence the emergence of bursty activity patterns.

Abstract

Inhomogeneous temporal processes in natural and social phenomena have been described by bursts that are rapidly occurring events within short time periods alternating with long periods of low activity. In addition to the analysis of heavy-tailed inter-event time distributions, higher-order correlations between inter-event times, called correlated bursts, have been studied only recently. As the possible mechanisms underlying such correlated bursts are far from being fully understood, we devise a simple model for correlated bursts by using a self-exciting point process with variable memory range. Here the probability that a new event occurs is determined by a memory function that is the sum of decaying memories of the past events. In order to incorporate the noise and/or limited memory capacity of systems, we apply two memory loss mechanisms, namely either fixed number or variable number of memories. By using theoretical analysis and numerical simulations we find that excessive amount of memory effect may lead to a Poissonian process, which implies that for memory effect there exists an intermediate range that will generate correlated bursts of magnitude comparable to empirical findings. Hence our results provide deeper understanding of how long-range memory affects correlated bursts.