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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).

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  • $\begingroup$ 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. $\endgroup$
    – Will Gu
    Commented Dec 7, 2016 at 19:01

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You should recover the forecast to the variance level and apply the qlike loss.

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