  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.
