4.4 Article

Scoring interval forecasts: Equal-tailed, shortest, and modal interval

Journal

BERNOULLI
Volume 27, Issue 3, Pages 1993-2010

Publisher

INT STATISTICAL INST
DOI: 10.3150/20-BEJ1298

Keywords

Elicitability; forecast evaluation; interval forecast; modal interval; predictive performance; scoring function

Funding

  1. Klaus Tschira Foundation
  2. German Research Foundation (DFG) [RTG 1953]

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This study examines the elicitable properties of different types of predictive intervals, finding that the equal-tailed interval and the modal interval are elicitable, while the shortest interval is not. These results provide guidance in interval forecast evaluation and support recent choices of performance measures in forecast competitions.
We consider different types of predictive intervals and ask whether they are elicitable, that is, are unique minimizers of a loss or scoring function in expectation. The equal-tailed interval is elicitable, with a rich class of suitable loss functions, though subject to translation invariance, or positive homogeneity and differentiability, the Winkler interval score becomes a unique choice. The modal interval also is elicitable, with a sole consistent scoring function, up to equivalence. However, the shortest interval fails to be elicitable relative to practically relevant classes of distributions. These results provide guidance in interval forecast evaluation and support recent choices of performance measures in forecast competitions.

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