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Probabilistic forecast determination
(2021) Nikologiannis, Christos; Νικολογιάννης, Χρήστος; Athens University of Economics and Business, Department of Statistics; Papastamoulis, Panagiotis; Karlis, Dimitrios; Demiris, Nikolaos
Probabilistic forecasts have gained significant ground nowadays compared to point forecasts due to the additional information they provide. In point forecasts, the main metric for evaluation is the accuracy of our model's point predictions. The goal of this work is to theoretically discuss probabilistic forecasts and present ways to evaluate their performance and statistical consistency. After an almost philosophical discussion on calibration and sharpness principles, which has been an old topic of research, a theoretical framework for scoring rules is presented with reference to a compilation of other works from the literature on the subject. The competing methods employed are logistic regression, with its regularized version versus tree-based methods, including Desicion trees, Random forests and Reinforcement learning trees. To highlight the add-on value of the scoring rules, hands-on applications of those scoring rules are conducted in binary classification problems to compare probabilistic forecasts evaluated upon simulated and real data in various dimensionality settings.