  Long-term temporal correlations observed in event sequences of natural and
social phenomena have been characterized by algebraically decaying
autocorrelation functions. Such temporal correlations can be understood not
only by heterogeneous interevent times (IETs) but also by correlations between
IETs. In contrast to the role of heterogeneous IETs on the autocorrelation
function, yet little is known about the effects due to the correlations between
IETs. In order to rigorously study these effects, we derive an analytical form
of the autocorrelation function for the arbitrary IET distribution in the case
with weakly correlated IETs, where the Farlie-Gumbel-Morgenstern copula is
adopted for modeling the joint probability distribution function of two
consecutive IETs. Our analytical results are confirmed by numerical simulations
for exponential and power-law IET distributions. For the power-law case, we
find a tendency of the steeper decay of the autocorrelation function for the
stronger correlation between IETs. Our analytical approach enables us to better
understand long-term temporal correlations induced by the correlations between
IETs.
