In the past I've done this kind of thing for a living. The general concept is to think of a model that would have some predictive power, then fit e.g. the first half of the data set to the model, and finally test to see whether the model has any predictive power on the second half of the data set.
If you haven't tried anything before, a good place to start is with ARMA models, (see e.g. AutoRegressive–Moving-Average model on wikipedia).