  We investigate the spectral and timing signatures of the internal-shock model
for blazars. For this purpose, we develop a semi-analytical model for the
time-dependent radiative output from internal shocks arising from colliding
relativistic shells in a blazar jet. The emission through synchrotron and
synchrotron-self Compton (SSC) radiation as well as Comptonization of an
isotropic external radiation field are taken into account. We evaluate the
discrete correlation function (DCF) of the model light curves in order to
evaluate features of photon-energy dependent time lags and the quality of the
correlation, represented by the peak value of the DCF. The almost completely
analytic nature of our approach allows us to study in detail the influence of
various model parameters on the resulting spectral and timing features. This
paper focuses on a range of parameters in which the gamma-ray production is
dominated by Comptonization of external radiation, most likely appropriate for
gamma-ray bright flat-spectrum radio quasars (FSRQs) or low-frequency peaked BL
Lac objects (LBLs). In most cases relevant for FSRQs and LBLs, the variability
of the optical emission is highly correlated with the X-ray and high-energy
(HE: > 100 MeV) gamma-ray emission. Our baseline model predicts a lead of the
optical variability with respect to the higher-energy bands by 1 - 2 hours and
of the HE gamma-rays before the X-rays by about 1 hour. We show that variations
of certain parameters may lead to changing signs of inter-band time lags,
potentially explaining the lack of persistent trends of time lags in most
blazars.
