  Typically, point forecasting methods are compared and assessed by means of an
error measure or scoring function, such as the absolute error or the squared
error. The individual scores are then averaged over forecast cases, to result
in a summary measure of the predictive performance, such as the mean absolute
error or the (root) mean squared error. I demonstrate that this common practice
can lead to grossly misguided inferences, unless the scoring function and the
forecasting task are carefully matched.
  Effective point forecasting requires that the scoring function be specified
ex ante, or that the forecaster receives a directive in the form of a
statistical functional, such as the mean or a quantile of the predictive
distribution. If the scoring function is specified ex ante, the forecaster can
issue the optimal point forecast, namely, the Bayes rule. If the forecaster
receives a directive in the form of a functional, it is critical that the
scoring function be consistent for it, in the sense that the expected score is
minimized when following the directive.
  A functional is elicitable if there exists a scoring function that is
strictly consistent for it. Expectations, ratios of expectations and quantiles
are elicitable. For example, a scoring function is consistent for the mean
functional if and only if it is a Bregman function. It is consistent for a
quantile if and only if it is generalized piecewise linear. Similar
characterizations apply to ratios of expectations and to expectiles. Weighted
scoring functions are consistent for functionals that adapt to the weighting in
peculiar ways. Not all functionals are elicitable; for instance, conditional
value-at-risk is not, despite its popularity in quantitative finance.
