  Temporal inhomogeneities observed in various natural and social phenomena
have often been characterized in terms of scaling behaviors in the
autocorrelation function with a decaying exponent $\gamma$, the interevent time
distribution with a power-law exponent $\alpha$, and the burst size
distributions. Here the interevent time is defined as a time interval between
two consecutive events in the event sequence, and the burst size denotes the
number of events in a bursty train detected for a given time window. In order
to understand such temporal scaling behaviors implying a hierarchical temporal
structure, we devise a hierarchical burst model by assuming that each observed
event might be a consequence of the multi-level causal or decision-making
process. By studying our model analytically and numerically, we confirm the
scaling relation $\alpha+\gamma=2$, established for the uncorrelated interevent
times, despite of the existence of correlations between interevent times. Such
correlations between interevent times are supported by the stretched
exponential burst size distributions, for which we provide an analytic
argument. In addition, by imposing conditions for the ordering of events, we
observe an additional feature of log-periodic behavior in the autocorrelation
function. Our modeling approach for the hierarchical temporal structure can
help us better understand the underlying mechanisms behind complex bursty
dynamics showing temporal scaling behaviors.
