I have a group ( only 20 of them, each one has 170 time pointers) of time series that I can consider as "GOOD", meaning, they have consistent statistical characteristics. I am not sure how they are generated, but they are biological data, so I assume the current point is not independent to its temporal neighbors. I think ARMA model is the good direction. So I fit the group of time series with ARAM model and get the order (p,q). Note that unfortunately, I don't have any sample from the "BAD" distribution, all other time series that deviates largely from the "GOOD" ones can be considered as "BAD".
Now given a new time series, how can I measure the likelihood that it is generated by ARMA(p,q) ? Or anything that's proportional to the likelihood. I don't think ARMA itself can infer this probability, but I wonder if there are some other useful techniques that I am not aware of. Or is there any other approach I can take to tackle the problem?