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Abstract:
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Effective point forecast can be obtained in one of two ways, namely, by disclosing the scoring function to the forecaster, and then using the Bayes rule to find the optimal point forecast, or by requesting a specific functional of the forecaster's predictive distribution, and then using a score function that is consistent with the functional. In most cases, Bayes rules exist and are usually unique. However, the simulation study in this paper indicates that the Bayes rule is not robust, in the sense that it is affected by outliers or small departures from model assumptions, and it is no longer optimal under the pre-specified score function. In this paper, we aim at creating robust forecasting in one of the two complementary ways, i.e., by using some "robust" scoring rules (such as down-weighting terms in the scoring function that are affected by outliers) and then finding the associated optimal forecasts, or by designing a robust forecast such that a pre-selected behavior of a bounded influence function is achieved, and then seeking scoring rules that are consistent with the designed robust forecast. This framework works for both point forecasting and probabilistic forecasting.
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