Probabilistic forecast reconciliation: Properties, evaluation and score optimisation
نویسندگان
چکیده
We develop a framework for forecasting multivariate data that follow known linear constraints. This is particularly common in where some variables are aggregates of others, commonly referred to as hierarchical time series, but also arises other prediction settings. For point forecasting, an increasingly popular technique reconciliation, whereby forecasts made all series (so-called base forecasts) and subsequently adjusted cohere with the extend reconciliation from probabilistic forecasting. A novel definition developed used construct densities draw samples reconciled forecast. In elliptical case, we prove true predictive distributions can be recovered using even when location scale predictions chosen arbitrarily. Reconciliation weights estimated optimise energy or variogram score. The log score not considered since it improper comparing unreconciled forecasts, result proved this paper. Due randomness objective function, optimisation uses stochastic gradient descent. method improves upon simulated empirical data, models severely misspecified. milder misspecification, extending methods results similar performance optimisation.
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ژورنال
عنوان ژورنال: European Journal of Operational Research
سال: 2023
ISSN: ['1872-6860', '0377-2217']
DOI: https://doi.org/10.1016/j.ejor.2022.07.040