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Elicitability is a mathematical property, satisfied by some risk measures, that allows for the ranking of risk models’ performance. If a risk measure is elicitable, then there exists a scoring function for that risk measure that can be used for comparative tests on models.
Elicitability has been proven a useful property for model selection, estimation, forecast comparison and forecast ranking.
Crucially, value-at-risk (VAR) is elicitable, while expected shortfall (ES) is not. Researchers have long debated over the connection between elicitability and backtestability, fuelled by the adoption of expected shortfall for the calculation of capital requirements.
While doubts were cast on the backtestability of non-elicitable risk measures, recent studies confirmed that lack of elicitability prevents strict backtesting, although an approximate backtesting is generally possible for non-elicitable risk measures when certain conditions are met, as in the case of variance and ES.
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