Motivated by the common problem of constructing predictive distributions for daily asset returns over horizons of one to several trading days, this article introduces a new model for time series. This model is a generalization of the Markov normal mixture model in which the mixture components are themselves normal mixtures, and it is a specific case of an artificial neural network model with two hidden layers. The article uses the model to construct predictive distributions of daily S&P 500 returns 1971–2005 and one-year maturity bond returns 1987–2007. For these time series the model compares favorably with ARCH and stochastic volatility models. The article concludes by using the model to form predictive distributions of one- to ten-day returns during volatile episodes for the S&P 500 and bond return series. Copyright © 2010 John Wiley & Sons, Ltd.