We use a nonlinear, nonparametric method to forecast unemployment rates. This method is an extension of the nearest-neighbor method but uses a higher-dimensional simplex approach. We compare these forecasts with several linear and nonlinear parametric methods based on the work of Montgomery et al. (1998) and Carruth et al. (1998). Our main result is that, due to the nonlinearity in the data-generating process, the nonparametric method outperforms many other well-known models, even when these models use more information. This result holds for forecasts based on quarterly and on monthly data.