# QLIKE loss function to evaluate forecasting model of log(realized volatility)

I use QLIKE as loss function to evaluate the forecasting performance of a RV realized volatility model.

QLIKE = log $h$ + $\frac{\hat{\sigma}^2}{h}$

where $h$ is volatility forecast and $\hat{\sigma}^2$ is the ex post value of volatility (realized volatility computed with intraday returns).

If I proxy volatility with log(RV), what are $h$ and $\hat{\sigma}^2$ in the QLIKE? The forecast and ex post value of log(RV) or the forecast and ex post value of RV? If I keep the logs, $h$ is sometimes negative and I have the problem of a log of a negative quantity. I'm not sure if I should come back to RV with exponential of the forecast of log(RV) or I should, for instance, replace log(RV) with log(1+RV).

• I think you meant $\sigma^2$ to be variance. What kind of model are you using for vol forecast? Negative vol is usually eliminated from model when possible, since the negative vol does make much sense. Commented Dec 7, 2016 at 19:01