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Abstract:
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Popular reconciling hierarchical forecast methods such as MinT, assume joint Normal distributions across all levels of hierarchies. However, this assumption is often not flexible enough to accomodate real-world situations. Aspects of the joint distribution of forecasts, such as discrete values, non-negativeness, correlation, asymmetry, long tails and custom weights, suggest that a different objective function may be more appropriate and more general. In this talk, we propose a reconciliation procedure based on minimizing the cross entropy between reconciled and unreconciled composite likelihood. This procedure guarantees reconciled first and second moments for generic distributional forecasts, while allowing customized marginal distributional assumptions on different levels, including a custom weighting scheme to reflect relative importance of multiple levels. In case of Gaussian errors, the full distributional forecasts are reconciled. We evaluate the performance of this procedure on data with non-negative support and compare with other distributional reconciliation methods.
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