One of my college professors wrote one of the first programs to do this (about 15 years ago). It was what is called a hybrid system, a rule-based program that was tuned by a NN. If I remember correctly it could predict short-term movements with about 80% accuracy.

One of the best hedge funds in the world (100% annual returns before fees) is entirely computationally based, so that general approach has merit. Not sure if neural networks are employed specifically in that case, however.