I use QLIKE as loss function to evaluate the forecasting performance of a RV realized volatility model. QLIKE = log hh + σ^2h\frac{\hat{\sigma}^2}{h} where hh is volatility forecast and σ^2\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 hh and σ^2\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, hh 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).