In the starburst model for active galactic nuclei (AGN), the observed broad emission lines and their variability are generated by compact, strongly radiative supernova remnants. These compact remnants are expected to occur preferentially in the central region of massive early-type galaxies undergoing a nuclear burst of star formation. This paper deals with the time-dependent processes that occur prior to thin shell formation in a rapidly radiating supernova remnant, i.e. as it achieves maximum luminosity. This process, which has a typical time-scale of a few weeks and involves energies of about 5 per cent of the total explosion energy, produces time delays between the continuum and line emission, line and contiuum luminosities, and emission-line ratios with values similar to those observed in low-luminosities, and emission-line ratios with similar values to those observed in low-luminosity AGN. The predicted delays are shorter for the high-ionization lines than for the low-ionization lines. We also predict the occurrence, after shell formation, of shorter flares with little or no lag between continuum and lines. The models are compared with the results from the extensive monitoring campaign of NGC 5548 to show that the compact supernova remnant model is capable of giving an accurate and detailed description of the temporal behaviour of the broad-line region as well as accounting for all of the intrinsic parameters of the broad-line region with essentially only one free parameter: the density of the ambient medium.