Dynamic linear models with discounting are state-space models that are sufficiently flexible interpretable, and computationally efficient. As such they are increasingly applied in economics and finance. Successful modeling and forecasting with such models depends on an appropriate choice of the discount factor. In this work we develop an adaptive approach to sequentially estimate this parameter, which relies on the minimisation of the one-step-ahead forecast error. Simulated data and an in-depth empirical application to the problem of forecasting quarterly UK house prices shows that our approach can achieve significant improvement in forecast accuracy at a computational cost that is orders of magnitude smaller than approaches based on sequential Monte Carlo. We also conduct an extensive evaluation of diverse forecast combination methods on the task of predicting UK house prices. Our results indicate that a recent density combination method can substantially improve forecast accuracy.