One of the things that I started looking at when I first started trading was Neural Networks. I got a book by Timothy Masters called Signal and Image Processing with Neural Networks, and I started working with his software to try to forecast the stock market.
What I did was take past values, and then use the past values to try to predict the future values. This method is something called working with 'lags', or values that are in the past, that lag the current value, or future values.
I quickly found that this type of prediction isn't easy, and that it required a lot of of computer time to do. But I had promising results -- I found that it was possible to develop training and test sets that were better than 50% accurate -- 50% being random chance. I developed neural networks that were 55%-65% accurate, but when I actually tried to trade with these, it was very hard to actually time the entries and exits for profitable trading.
Neural networks map values to values with a mapping that works like the neural networks in the body of people or mammals.
For example, here is an example of a simple neural networks.
input 1 x1-\
input 2 x2-\
input 3 x3--y output.
input 4 x4-/
input 5 x5-/
It maps to a function where a weight can be assigned to each x variable, x1, etc., and the y, output variable. The weights can be trained by a variety of methods. One of these methods is something called backpropagation, where the errors are measured, and back measured to each of the weights, and the weights are adjusted. It originally took a long time to train these types of networks, but with faster processors, it got easier.
