In this paper, we examine the Meese–Rogoff puzzle from a different perspective: out-of-sample interval forecasting. While most studies in the literature focus on point forecasts, we apply semiparametric interval forecasting to a group of exchange rate models. Forecast intervals for 10 OECD exchange rates are generated and the performance of the empirical exchange rate models are compared with the random walk. Our contribution is twofold. First, we find that in general, exchange rate models generate tighter forecast intervals than the random walk, given that their intervals cover out-of-sample exchange rate realizations equally well. Our results suggest a connection between exchange rates and economic fundamentals: economic variables contain information useful in forecasting distributions of exchange rates. We also find that the benchmark Taylor rule model performs better than the monetary, PPP and forward premium models, and its advantages are more pronounced at longer horizons. Second, the bootstrap inference framework proposed in this paper for forecast interval evaluation can be applied in a broader context, such as inflation forecasting.