Comparing GARCH Specifications with AIC and BIC

Summary

The document explains when Akaike and Bayesian information criteria can be used to compare sGARCH, eGARCH, and gjrGARCH models fitted to the same time series. The stated conditions are that each model uses the same observations, parameters are estimated by maximum likelihood, and the sample is sufficiently large relative to the number of model parameters. The models do not need to be nested for AIC or BIC comparisons.

These criteria provide a relative basis for preferring among candidates, not proof that a selected model is the true data-generating process. The appropriate choice also depends on the model’s intended use, and the true specification may be absent from the candidate set. The document does not give a worked calculation or compare predictive performance out of sample, so information criteria should be read as model-selection guidance rather than a complete evaluation.

Key ideas

• AIC or BIC can compare candidate GARCH specifications fitted to the same dataset.
• The comparison assumes maximum-likelihood estimation and a sample large enough relative to model complexity.
• Candidate models do not have to be nested for these information criteria to be compared.
• Information criteria rank candidates but do not show that any candidate is the true model.
• Model choice depends on the intended use, and predictive checks may provide additional evidence.

Tags

# Information criteria via different GARCH models


# Information criteria via different GARCH models












I have a question about comparison of different GARCH models via information criteria.

I use rugarch package. So, let's have 3 model types: "sGARCH", "eGARCH", "gjrGARCH". I fit all 3 type models for same time series, for example, for p=q=1. Could I use IC (BIC, for example) for best model selection among these 3 types? If not, what's the best method for this?

Thank you.

## Answer by Eldioo (score 2, accepted)

https://quant.stackexchange.com/a/34900

In short: Yes, you can use the $BIC$ (and $AIC$) information criteria, assuming the following:

- All models are applied on exactly the same data set.

- All model parameters are estimated via maximum likelihood estimation.

- Your sample size is much bigger, than the amount of parameters in the models (as GARCH models don't have many parameters, this will probably be no issue)

Even though it is often claimed, the compared models don't need to be nested for the $AIC$ and $BIC$ to be valid.

Lastly, note that there is no "best" way in model selection. It all depends on the purpose of the model that you are looking for - usually, in a real life setting, the true model isn't even one of the candidates. However, $AIC$ and $BIC$ can usually give you a good idea, which of the models is preferable.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.