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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?

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  • $\begingroup$ What do you do with volatility? Can you seriously claim that you absolutely in no way use it in any kind of forward looking fashion? $\endgroup$
    – Aksakal
    Commented May 12, 2014 at 15:33
  • $\begingroup$ I`m setting up a dynamic scenario analysis framework to evaluate the performance of Value at Risk and Expected Shortfall estimation methods. For better realism I want to create several quiet and several stress scenarios where the conditional variance and mean are extracted from quiet and stressful periods in real-world time series. So I can make sure that typical autocorrelation patterns are part of my framework, but also regime jumps as well as slower regime shifts. Only therefore I need the vola. $\endgroup$
    – Joz
    Commented May 12, 2014 at 15:40

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You clearly are using volatilities in the out-of-sample context, so out-of-sample testing of GARCH is required. If you are in banking, then model validation will most likely request it.

The volatility is used to build the scenarios, which are used to test the VaR. The VaR is a foreward looking measure, it measures the risk of your portfolio in coming days. Therefore, your volatility is used in the foreward looking context, in my opinion. Hence, the out-of-sample is in order.

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  • $\begingroup$ Hmm, I'm definitely not using the model out of sample. And I'd argue that I also don't use the estimated vola out of sample. I rather augment the in-sample-period with some add-ons (e.g. using a mixture distribution which was not part of the GARCH estimation and some adaptation of the vola and mean level close to regime switching points for smoother progression). So I'm using the in-sample-period a bit out of context. I'm still not sure if this is a classical "out-of-sample context". One might call it an "out-of-context-sample" :) $\endgroup$
    – Joz
    Commented May 12, 2014 at 16:42

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