Summary This paper illustrates the usefulness of sequential Monte Carlo (SMC) methods in approximating dynamic stochastic general equilibrium (DSGE) model posterior distributions. We show how the tempering schedule can be chosen adaptively, document the accuracy and runtime benefits of generalized data tempering for ‘online’ estimation (that is, re-estimating a model as new data become available), and provide examples of multimodal posteriors that are well captured by SMC methods. We then use the online estimation of the DSGE model to compute pseudo-out-of-sample density forecasts and study the sensitivity of the predictive performance to changes in the prior distribution. We find that making priors less informative (compared with the benchmark priors used in the literature) by increasing the prior variance does not lead to a deterioration of forecast accuracy.