This paper presents some research on the application of artificial neural networks to economic modeling. The Efficient Markets Hypothesis (EMH) states that at any time, the price of a security fully captures all known information about that stock, so the price behaves like a random walk in time, except when there are changes in information. We test whether a nonlinear statistical method, error back propagation, can do better than chance in forecasting stock trends. An error back propagation model is estimated at different levels of time aggregation (daily and monthly) on stock price and stock index returns. This paper brings forth some new and encouraging results on the ability of neural network models to predict the direction of stock price movements and to account for some of the nonlinearities found in stock return data.