We outline in turn criticisms made by econometricians of the methods used in empirical business-cycle research and then criticisms made by business-cycle researchers of some methods used by econometricians. The aim is to clarify and in some cases correct these criticisms. Overall there is no conflict in using rigourous statistical procedures to study modern dynamic stochastic general equilibrium models. We also provide a concise bibliography of recent research on statistical methods for business-cycle models.