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Testing the reliability of forecasting systems

Bröcker, J. (2023) Testing the reliability of forecasting systems. Journal of Applied Statistics, 50 (1). pp. 106-130. ISSN 1360-0532

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To link to this item DOI: 10.1080/02664763.2021.1981833


The problem of statistically evaluating forecasting systems is revisited. The forecaster claims the forecasts to exhibit a certain nominal statistical behaviour; for instance, the forecasts provide the expected value (or certain quantiles) of the verification, conditional on the information available at forecast time. Forecasting systems that indeed exhibit the nominal behaviour are referred to as reliable. Statistical tests for reliability are presented (based on an archive of verification–forecast pairs). As noted previously, devising such tests is encumbered by the fact that the dependence structure of the verification–forecast pairs is not known in general. Ignoring this dependence though might lead to incorrect tests and too-frequent rejection of forecasting systems that are actually reliable. On the other hand, reliability typically implies that the forecast provides information about the dependence structure, and using this in conjunction with judicious choices of the test statistic, rigorous results on the asymptotic distribution of the test statistic are obtained. These results are used to test for reliability under minimal additional assumptions on the statistical properties of the verification–forecast pairs. Applications to environmental forecasts are discussed. A python implementation of the discussed methods is available online.

Item Type:Article
Divisions:Interdisciplinary Research Centres (IDRCs) > Centre for the Mathematics of Planet Earth (CMPE)
Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
ID Code:100790
Publisher:Taylor & Francis


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