Let me first say that I am a CS person and my knowledge about statistics is quite basic. I am trying to see what predictive analysis to use for a problem I am trying to solve. I will try to make my problem general also so that anyone can benefit from the question. Basically, I have a group of objects that I am watching over a certain period of time. By the end of that period, some objects remain unchanged, other objects are modified by a small amount, while other ones change completely. I am trying to look at a small history of these objects and predict how they will change in the future. I want to identify what are the parameters that affect their future behavior and how they affect their future behavior. I dont know what part of statistics should I look into. I think it is important to say that the outcome is discrete. I want to classify those objects into "stable", "change by a small value", or completely change.
The main portion of your question can be answered by : Investigate ARMA models which can be useful to analyze and predict a time series. Arbitrary classification is yet another matter. One would have to specify the classification rules and the use the forecasts vis-a-vis recent values in order to bucket the series into your three classes.