Making and Evaluating Point Forecasts

Typically, point forecasting methods are compared and assessed by means of an error measure or scoring function, with the absolute error and the squared error being key examples. The individual scores are averaged over forecast cases, to result in a summary measure of the predictive performance, suc...

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Vydané v:	Journal of the American Statistical Association Ročník 106; číslo 494; s. 746 - 762
Hlavný autor:	Gneiting, Tilmann
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Alexandria, VA Taylor & Francis 01.06.2011 American Statistical Association Assoc Taylor & Francis Ltd
Predmet:	Applications Bayes rule Bayesian analysis Bregman function Conditional value-at-risk (CVaR) Decision theory Economic forecasting Elicitability Error Estimation Exact sciences and technology Expectation Expectations Expectile Financial theory Forecasting Forecasting techniques Function Functional analysis General topics Inference from stochastic processes; time series analysis Insurance, economics, finance Mathematical analysis Mathematical functions Mathematics Mean Mean square errors Measurement Median Methodology Mode Point forecasts Popularity Probabilities Probability and statistics Probability distributions Probability forecasts Proper scoring rule Quantile Review Article Rules Sciences and techniques of general use Scores Special functions Statistical forecasts Statistical functional Statistics Time series forecasting Weather forecasting Weighting Mean Conditional distribution Generalized linear model Error estimation Predictive distribution Prediction theory Median Statistical functional Stochastic process Bregman function Absolute error Forecasting theory Elicitability Quantile Bayes estimation Bayes rule Finance Predictive measure Conditional value-at-risk (CVaR) Mode Statistical estimation Proper scoring rule Statistical decision Mean estimation Functional Statistical method Statistical regression Expectile Decision theory Weight function Filtering theory Mean error
ISSN:	0162-1459, 1537-274X
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Shrnutí:	Typically, point forecasting methods are compared and assessed by means of an error measure or scoring function, with the absolute error and the squared error being key examples. The individual scores are averaged over forecast cases, to result in a summary measure of the predictive performance, such as the mean absolute error or the 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.
Bibliografia:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23
ISSN:	0162-1459 1537-274X
DOI:	10.1198/jasa.2011.r10138