# evaluation of volatility models using loss functions

This question has two parts, What is the state of the art in an academic or public knowledge sense of volatility forecast model evaluation?

Since there are many methods out in the wild, and do correct me if I am wrong but I haven't been able to find a complete list or any list for that matter of methods used so I'd like to start that here. It is very popular to use many of the different loss functions with arma-garch style models.

Some methods commonly used include:

Mean Absolute Error

$MAE = n^{-1} \sum_{t=1}^n | \sigma_t - h_t|$

$\boldsymbol{R^2 \ log}$

$R^2LOG = n^{-1} \sum_{t=1}^n (log(\sigma_t^2 h_t^{-2}))^2$

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Possible duplicate of quant.stackexchange.com/questions/8056/… –  Jase Oct 23 '13 at 17:39
@Jase I guess the wording makes it seem similar, but this is more specific i'll update –  pyCthon Oct 23 '13 at 23:27

Mincer-Zarnowitz is the standard for evaluating out of sample , how ever the $R^2$ based evaluation isn't suitable for comparison among different volatility forecast models. example, good $R^2$ and poor biased forecast.. –  pyCthon Oct 24 '13 at 2:10
I've dug deeper and it seems $R^2log$ maybe something interesting –  pyCthon Oct 24 '13 at 2:18