Making and Evaluating Point Forecasts

Making and Evaluating Point Forecasts

March 9, 2010 | Tilmann Gneiting
Tilmann Gneiting discusses the evaluation of point forecasts, emphasizing the importance of aligning scoring functions with forecasting tasks. He argues that common practices, such as using absolute or squared error, can lead to misleading inferences if not carefully matched to the task. Effective point forecasting requires specifying a scoring function a priori or directing forecasters to report specific statistical functionals like the mean or quantile. A scoring function is consistent for a functional if it minimizes expected loss when following that functional. Elicitable functionals, such as expectations, quantiles, and ratios of expectations, have consistent scoring functions, while others like conditional value-at-risk are not. The paper introduces the concept of consistency and elicitability, showing that consistent scoring functions induce proper scoring rules and link Bayes rules to consistent functionals. It also presents a decision-theoretic framework for evaluating point forecasts, demonstrating that consistent scoring functions are dual to optimal point forecasts. The paper concludes that effective point forecasting requires either a priori specification of the scoring function or a directive to report specific functionals, ensuring meaningful evaluation.Tilmann Gneiting discusses the evaluation of point forecasts, emphasizing the importance of aligning scoring functions with forecasting tasks. He argues that common practices, such as using absolute or squared error, can lead to misleading inferences if not carefully matched to the task. Effective point forecasting requires specifying a scoring function a priori or directing forecasters to report specific statistical functionals like the mean or quantile. A scoring function is consistent for a functional if it minimizes expected loss when following that functional. Elicitable functionals, such as expectations, quantiles, and ratios of expectations, have consistent scoring functions, while others like conditional value-at-risk are not. The paper introduces the concept of consistency and elicitability, showing that consistent scoring functions induce proper scoring rules and link Bayes rules to consistent functionals. It also presents a decision-theoretic framework for evaluating point forecasts, demonstrating that consistent scoring functions are dual to optimal point forecasts. The paper concludes that effective point forecasting requires either a priori specification of the scoring function or a directive to report specific functionals, ensuring meaningful evaluation.
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