Making and Evaluating Point Forecasts

Making and Evaluating Point Forecasts

March 9, 2010 | Tilmann Gneiting
The paper discusses the evaluation and comparison of point forecasts using scoring functions, highlighting the common practice of using error measures like absolute or squared errors. However, this approach can lead to misleading inferences unless the scoring function is carefully matched to the forecasting task. Effective point forecasting requires either specifying a scoring function in advance or providing a statistical functional, such as the mean or quantile, to which the forecaster should adhere. The paper introduces the concepts of consistency and elicitability, where a scoring function is consistent for a functional if it minimizes the expected score when following the functional. Not all functionals are elicitable, meaning there may not exist a scoring function that strictly minimizes the score. The paper provides examples of elicitable functionals, including expectations, ratios of expectations, quantiles, and expectiles, and discusses the properties of weighted scoring functions. It concludes with a call for a more principled approach to point forecasting, emphasizing the importance of specifying the scoring function or the functional to be elicited.The paper discusses the evaluation and comparison of point forecasts using scoring functions, highlighting the common practice of using error measures like absolute or squared errors. However, this approach can lead to misleading inferences unless the scoring function is carefully matched to the forecasting task. Effective point forecasting requires either specifying a scoring function in advance or providing a statistical functional, such as the mean or quantile, to which the forecaster should adhere. The paper introduces the concepts of consistency and elicitability, where a scoring function is consistent for a functional if it minimizes the expected score when following the functional. Not all functionals are elicitable, meaning there may not exist a scoring function that strictly minimizes the score. The paper provides examples of elicitable functionals, including expectations, ratios of expectations, quantiles, and expectiles, and discusses the properties of weighted scoring functions. It concludes with a call for a more principled approach to point forecasting, emphasizing the importance of specifying the scoring function or the functional to be elicited.
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Understanding Making and Evaluating Point Forecasts