  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.
