Context. High-resolution Very Long Baseline Interferometry (VLBI) observations of active galactic nuclei revealed traveling and stationary or quasi-stationary radio components in several blazar jets. The traveling radio components are, in general, interpreted as shock waves generated by pressure perturbations injected at the jet nozzle. The stationary features can be interpreted as recollimation shocks in nonpressure matched jets if they show a quasi-symmetric bump in the spectral index distribution. In some jets there may be interactions between the two kinds of shocks. These shock-shock interactions are observable with VLBI techniques and their signature should also be imprinted on the single-dish light curves. Aims. In this paper, we investigate the spectral evolution produced by the interaction between a recollimation shock with traveling shock waves to address the question of whether these interactions contribute to the observed flares and what their signature in both single-dish and VLBI observations looks like. Methods. We performed relativistic hydrodynamic simulations of overpressured and pressure-matched jets. To simulate the shock interaction we injected a perturbation at the jet nozzle once a steady state was reached. We computed the nonthermal emission, including adiabatic and synchotron losses, resulting from the simulation. Results. We show that the injection of perturbations in a jet can produce a bump in emission at GHz frequencies previous to the main flare, which is produced when the perturbation fills the jet in the observer's frame. The detailed analysis of our simulations and the nonthermal emission calculations show that interaction between a recollimation shock and traveling shock produce a typical and clear signature in both the single-dish light curves and in the VLBI observations: the flaring peaks are higher and delayed with respect to the evolution of a perturbation through a conical jet. This fact can allow us to detect such interactions for stationary components lying outside of the region in which the losses are dominated by inverse Compton scattering.