Wherever I read about performance checks of GARCH models people stress the need for out-of-sample testing (e.g. out-of-sample forecast evaluation, out-of-sample refitting and checking for the significance and value of the parameters etc.).
Now I have an application of a GARCH model where the model is only needed to extract the volatility of the sample which is also used for model fitting. I don't want to interpret or generalize the model, and I don't want to do out-of-sample forecasting. After having the volatility I throw the model away.
In this case I'd say that out-of-sample evaluation makes absolutely no sense. A totally overfitted model would be just the right thing as long as the in-sample-performance is alright (I certainly will check the stability of the parameter estimates for a given sample size using monte carlo simulations!). Do you think that this is right, or am I missing some important detail in my thinking?