I’ve been doing a lot of R coding with GARCH for my dissertation, I'm coming to the end of my writeup now but have hit a bit of a wall.

Obviously, gjrGARCH, apARCH and E-GARCH all allow for asymmetric impacts due to their model specifications, some done with log values and others with dummy variables.

But is there any specific reasons or examples in using the models in which one would be more preferable than the other? It's been impossible to find any reason to this online, appreciate any help.

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In GARCH modelling, one typically pursues either descriptive accuracy or predictive accuracy.

  • If you want to describe the data generating process as accurately as you can, you would choose the model that does that. You would look at the standardized residuals and inspect whether they are i.i.d. with the assumed distribution.
  • If you want to forecast future observations and estimate their probabilistic characteristics such as variance or quantiles, you would choose the model that is expected to do that best. You would look at AIC or use rolling or expanding windows and inspect out-of-sample forecast errors.

Even though all of the models share the property of being able to account for asymmetry, they are not the same. Hence, you may expect that one of them will fit your goal better than the others.

  • $\begingroup$ There is no difference between the two approaches other than the error functions used. They are both prediction. This distinction is bogus as I have been arguing for a long time. $\endgroup$ Mar 21, 2021 at 7:46
  • $\begingroup$ @CagdasOzgenc, incorrect. Description only requires a good in-sample fit, and that is demonstrably different from good predictive accuracy which requires good out-of-sample fit. But out of curiosity, would you mind sharing any of your posts where you argue otherwise? $\endgroup$ Mar 21, 2021 at 8:09
  • $\begingroup$ For example my comment under this post stats.stackexchange.com/a/448526/20980. You can fit an elephant in sample, but I think we we will all agree that there is one true DGP (which is a point hypothesis). As I wrote in that comment, in stats literature a model is a composite hypothesis. But this is a wrong way of looking at things. The difference between a descriptive accuracy vs a predictive accuracy is just a difference in error functions but always with respect to the true DGP (or its parameters). Any other measure such as in sample fit is simply an illusion. $\endgroup$ Mar 21, 2021 at 16:34

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