The crossing-point quantile: an optimal point-forecast in terms of ROC areas.

A point-forecast is defined as a single-value forecast expressed in the unit of a variable of interest. A deterministic forecast for 2m temperature at Vienna tomorrow is a point-forecast. Point-forecasts are required by some forecast users and for various applications. When an ensemble prediction system is at hand, a point-forecast can take the form of a distribution functional such as the ensemble mean or an ensemble quantile. In this context, we introduce a new type of point-forecast based on the concept of crossing-point forecast (Ben Bouallègue, 2021). We argue that this self-adaptive forecast should be better suited for some users than other point-forecasts. More precisely, we demonstrate that the so-called crossing-point quantile is an optimal forecast in terms of Pierce Skill Score (or equivalently in terms of area under the ROC curve) for any event of interest.  

Ben Bouallègue Z (2021), On the verification of the crossing-point forecast, Tellus A. DOI:10.1080/16000870.2021.1913007