Efficient probabilistic reconciliation of forecasts for real-valued and count time series

TL;DR

This paper introduces a novel probabilistic reconciliation method for hierarchical time series that ensures coherence across various forecast types, using an efficient sampling algorithm to improve speed and accuracy.

Contribution

It proposes a new conditioning-based approach and the Bottom-Up Importance Sampling algorithm for fast, coherent probabilistic forecasts across different data types.

Findings

Significant improvement over base probabilistic forecasts

Efficient sampling for discrete, continuous, or sample-based distributions

Applicable to various hierarchical time series

Abstract

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.