Dwarf nova outbursts result from enhanced mass transport through the accretion disc of a cataclysmic variable system. We assess the question of whether these outbursts are caused by an enhanced mass transfer from the late-type main sequence star onto the white dwarf (so-called mass transfer instability model, MTI) or by a thermal instability in the accretion disc (disc instability model, DIM). We compute non-LTE models and spectra of accretion discs in quiescence and outburst and construct spectral time sequences for discs over a complete outburst cycle. We then compare our spectra to published optical spectroscopy of the dwarf nova SS Cygni. In particular, we investigate the hydrogen and helium line profiles that are turning from emission into absorption during the rise to outburst. The evolution of the hydrogen and helium line profiles during the rise to outburst and decline clearly favour the disc-instability model. Our spectral model sequences allow us to distinguish inside-out and outside-in moving heating waves in the disc of SS Cygni, which can be related to symmetric and asymmetric outburst light curves, respectively.