Efficient probabilistic reconciliation of forecasts for real-valued and count time series
This work addresses the need for accurate and computationally efficient probabilistic reconciliation in fields like economics or supply chain, though it is incremental as it builds on existing reconciliation methods.
The paper tackles the problem of ensuring coherent probabilistic forecasts for hierarchical time series by proposing a conditioning-based approach and an efficient sampling algorithm, resulting in significant improvements over base forecasts in experiments.
Hierarchical time series are common in several applied fields. The forecasts for these time series are required to be coherent, that is, to satisfy the constraints given by the hierarchy. The most popular technique to enforce coherence is called reconciliation, which adjusts the base forecasts computed for each time series. However, recent works on probabilistic reconciliation present several limitations. In this paper, we propose a new approach based on conditioning to reconcile any type of forecast distribution. We then introduce a new algorithm, called Bottom-Up Importance Sampling, to efficiently sample from the reconciled distribution. It can be used for any base forecast distribution: discrete, continuous, or in the form of samples, providing a major speedup compared to the current methods. Experiments on several temporal hierarchies show a significant improvement over base probabilistic forecasts.