Evaluation of point forecasts for extreme events using consistent scoring functions

TL;DR

This paper introduces a method for comparing point forecasts in specific regions like tails or centers, ensuring non-hedged, region-specific evaluation with meaningful economic interpretations.

Contribution

It develops a region-focused scoring method that is non-hedged and provides decompositions aligned with decision-theoretic principles, enhancing forecast evaluation.

Findings

Method allows comparison of forecasts in targeted regions.

Decompositions provide interpretable scores based on economic regret.

Scores emphasize performance over user-defined decision thresholds.

Abstract

We present a method for comparing point forecasts in a region of interest, such as the tails or centre of a variable's range. This method cannot be hedged, in contrast to conditionally selecting events to evaluate and then using a scoring function that would have been consistent (or proper) prior to event selection. Our method also gives decompositions of scoring functions that are consistent for the mean or a particular quantile or expectile. Each member of each decomposition is itself a consistent scoring function that emphasises performance over a selected region of the variable's range. The score of each member of the decomposition has a natural interpretation rooted in optimal decision theory. It is the weighted average of economic regret over user decision thresholds, where the weight emphasises those decision thresholds in the corresponding region of interest.