I have been working on Neural Networks for various purposes lately. I have had great success in digit recognition, XOR, and various other easy/hello world\'ish applications.
Technically this is the same as your digit recognition - it is recognizing something and returning what it was...
Well - now your inputs are the previous steps (T-5 ... T-1) - and your output or outputs are the predicted steps (T0, T1...).
The mechanics in the ANN itself are the same - you will have to teach every layer for feature detection, correcting its reconstruction of the thing, so that it looks like what is actually going to happen.
(some more info about what do I mean: tech talk )