Comment:

This relative measure clearly tests the success of models when large movements are encountered. Figures 5u and 5m show that the tail emphasized GARCH(1,1) stands out in this respect. In figures 5u and 5m the mean log-likelihood value at the $50\%$ percentile level is the mean log-likelihood over all out-of-sample events. As we move to higher percentile levels, small movements are ignored. From this it is clear that the tail emphasized GARCH(1,1) slightly sacrifices performance in predicting small movements for better performance when movements are large.