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

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

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 $

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

Some methods commonly used include:

Mean Absolute Error

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

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

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

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

Some methods commonly used include

Mean Absolute Error

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

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

Some methods commonly used include:

Mean Absolute Error

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