  Blazars are among the most powerful extragalactic objects, as a sub-class of
active galactic nuclei. They launch relativistic jets and their emitted
radiation shows strong variability across the entire electro-magnetic spectrum.
The mechanisms producing the variability are still controversial and different
models have been proposed to explain the observed variations in multi-frequency
blazar light curves.We investigate the capabilities of the classical
shock-in-jet model to explain and reconstruct the observed evolution of flares
in the turnover frequency turnover flux density plane and their
frequency-dependent light curve parameters. With a detailed parameter space
study we provide the framework for future, detailed comparisons of observed
flare signatures with the shock-in-jet scenario. Based on the shock model we
compute synthetic single-dish light curves at different radio frequencies (2.6
to 345 GHz) and for different physical conditions in a conical jet (e.g.
magnetic field geometry and Doppler factor). From those we extract the slopes
of the different energy loss stages within the $\nu_\mathrm{m}$-$S_\mathrm{m}$
plane and deduce the frequency-dependence of different light curve parameters
such as flare amplitude, time scale and cross-band delays. The evolution of the
Doppler factor along the jet has the largest influence on the evolution of the
flare and on the frequency-dependent light curve parameters. The synchrotron
stage can be hidden in the Compton or in the adiabatic stage, depending mainly
on the evolution of the Doppler factor, which makes it difficult to detect its
signature in observations. In addition, we show that the time lags between
different frequencies can be used as an efficient tool to better constrain the
physical properties of these objects.
