Solved – How to correctly choose model based on BIC

bicmodel

I have a question about Bayesian Information Criteria. (GARCH models)

I have looked for so many hours but still very confused about this BIC especially a negative one. As far as I am concerned it is okay to have a BIC that is negative, but the interpretation of them are different in each book on website. I am not looking for sophisticated answer just a normal explanation as if you were to explain someone who is not math or statisticians.

Given same data,length and number of observation which model is better, based on BIC?

  1. -4.98749

  2. -4.995782

  3. -4.9864

I am using R software and running 3 models, GARCH-t, GJR model, and simple GARCH (1,1) model. So, I am trying to see which model is better, based only on BIC.
I have already concluded what model is better based on other factors but this makes me confused.

Best Answer

To at least make sure this has an answer:

The origin is effectively arbitrary. Smaller BIC (further left on the number line) is better by the criterion.

However, one ting to beware of if you compare BICs produced in different ways (using different models, or even the same models produced on different software) is the constants involved in the likelihood; it's common to drop constant terms, but if different models/software don't treat them in an equivalent way the BICs won't be comparable. Sometimes software will tell you exactly what computation is being performed in which case you can usually sort these issues out. When they don't, some detective work may be required. With the same model on different software this is usually easy to spot (and adjust for). With different models you may be able to figure out what is happening if there's a subset of models in common.

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