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.
