The likelihood that a time series is generated by certain ARMA(p,q) ?

Question

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?

Thanks

Answer 1

If you have 20 "good time series" one could test the hypothesis of a common set of parameters using the CHOW test which is incorporated in a commercial piece of software that I have helped develop . Alternatively one could write code to estimate the common parameters based upon the 20 samples and then perform the required F test. Now given that you have been able to conclude about a common set one could then introduce a "new time series" and test the hypothesis that the parameters from this new time series are similar i.e. not statistically significantly different from the common set.