We investigate the extent to which misperceptions about the economy can become self-reinforcing and thereby contribute to time-varying macroeconomic dynamics. To do so, we build a New Keynesian model with long-horizon expectations and dynamic predictor selection. Because agents solve multi-period optimisation problems (households maximise expected lifetime utility and firms maximise the discounted flow of future profits), their current decisions are influenced by expectations of the distant future and cannot in general be characterised by the familiar Euler equations that represent the rational expectations equilibrium of these models. We assume that agents have access to a set of alternative predictors that can be used to form expectations and choose among them based on noisy measures of their recent performance. This dynamic predictor selection generates endogenous fluctuations in the proportions of agents using each predictor, contributing to macroeconomic dynamics. We explore the behaviour of our model when agents have access to two simple predictors. One of the predictors is consistent with a mistaken belief that macroeconomic variables are more persistent than implied by the fundamental shocks hitting the economy. We show that the presence of a ‘persistent predictor’ can lead to changes in beliefs which are self-reinforcing, giving rise to endogenous fluctuations in the time-series properties of the economy. Moreover, we show that such fluctuations arise even if we replace the ‘persistent predictor’ with learning under constant gain.