We perform a comprehensive examination of the recursive, comparative predictive performance of linear and nonlinear models for UK stock and bond returns. We estimate Markov switching, threshold autoregressive (TAR) and smooth transition autoregressive (STR) regime switching models and a range of linear specifications including models with GARCH type specifications. Results demonstrate UK asset returns require nonlinear dynamics to be modelled with strong evidence in favour of Markov switching frameworks. Our results appear robust to the choice of sample period, changes in loss functions and to the methodology employed to test for equal predictive accuracy. The key findings extend to a similar sample of US data. © John Wiley & Sons Ltd and the Department of Economics, University of Oxford 2013.