seemingly similar models are determined to be similar, while LogS penalizes small differences in the probability tails very hard, even though these differences may not be of importance to the forecaster. As a d
This allows the forecaster to incorporate the relative costs of under versus over-prediction.Footnote7 It is well-known that this loss function elicits the τ-quantile of a random variable. Technically, the forecasting problem in this article (and in the CAViaR literature) is formulated as ...