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.
There is a kind of neural networks named recurrent neural networks (RNNs. One advantage of using these models is you do not have to define an sliding window for the input examples. A variant of RNNs known as Long-Short Term Memory (LSTM) can potentially take into account many instances in the previous time stamps and a "forget gate" is used to allow or disallow remembering the previous results from the previous time stamps.