Time-series analysis is important to a wide range of disciplines transcending both the physical and social sciences. Statistical models have sound theoretical bases and have been successfully used in a number of problem domains. More recently, machine-learning models such as neural networks have been suggested as offering potential for time-series analysis. Results of neural network empirical testing have thus far been mixed. This paper proposes melding useful parameters from the statistical ARIMA model with neural networks of two types: multilevel perceptrons (MLPs) and radial basis functions (RBFs). Tests are run on a range of time-series problems that exhibit many common patterns encountered by analysts. The results suggest that hybrids of the type proposed may yield better outcomes than either model by itself.