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I'm writing my thesis and will sketch the scenario I try to research: I have data for my GARCH model from two periods. The input is the same, as is the length (1y). I want to compare both the outcome of both models (from different periods) to see if there's a significant change or difference between these 2 periods. The division is made by a historic occurrence.

The only thing I can find is comparisons of the best fit of types of GARCH models for 1 time series, which I'm not interested in. Who can help me provide how I can compare the outcomes in a meaninful way? Any literature? Thanks in advance!

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You could build a GARCH model for the combined data from both periods and inspect whether the standardized residuals violate any assumptions. If they do not, there is no indication that the data generating processes (DGPs) in the two periods are different. If they do, you could make the model richer by adding some dummies and/or interaction terms to allow for different dynamics in the two periods. You would again inspect whether the assumptions are met. If you have done a good job in model specification for each period, they will be. You could then evaluate the effect sizes and the statistical significance of these additional effects. They would be informative of how the characteristics of the DGPs differ between the periods.

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  • $\begingroup$ Thanks for your answer, much appreciated. Saw the introduction of a 0/1 dummy to mark the periods somewhere else too, only doubted how to derive any valuable information from this. Would it also be possible to test both periods separately for violations. If they both meet all conditions I can then derive a conclusion for the full sample as well. Depending on if the full model meets the assumptions or not? I'm a business student not that familiar with modeling, so I'm trying to keep the models relatively simple. Introducing a lot of other terms (no idea which) will overcomplicate it for me. $\endgroup$ – Student101 Jun 30 at 23:05
  • $\begingroup$ @Student101, I understand the fear of overcomplication, but I think simplifying the models beyond what I suggest will likely make their comparison analytically intractable. So you can save some effort in model building, but you will have to compensate for that by extra effort on deriving analytical results for comparing the simpler models. The latter can be really hard. Regarding valuable information, what do you mean? The interpretation is easy. E.g. add a simple period-specific dummy to see if the unconditional variance has changed from one period to another. $\endgroup$ – Richard Hardy Jul 1 at 6:38
  • $\begingroup$ @Student101, Look at its effect size (point estimate) and statistical significance to evaluate how big the difference is and whether it is distinguishable from random noise on a chosen confidence level. $\endgroup$ – Richard Hardy Jul 1 at 6:39
  • $\begingroup$ Thanks so much, this is indeed the idea of what I was going for. I already wanted to compare the point estimates, but still do not see how I can derive a conclusion from the difference. I can only state that one is higher than the other? Or am I missing something. The introduction of a confidence level to check against random noise is an important addition I had not thought about and will implement. $\endgroup$ – Student101 Jul 1 at 14:15
  • $\begingroup$ @Student101, if the point estimate of a dummy or an interaction is large, the difference seems large. You have a number there, so you can interpret it. If it is statistically significant, you have an indication it is unlikely to be due to chance. These interpretations are not specific to GARCH models, they are pretty general. $\endgroup$ – Richard Hardy Jul 3 at 9:52

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