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

arXiv: https://arxiv.org/abs/2210.02286 · HTML: https://mlsanity.com/paper/2210.02286/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 46 references that are in the map.
- First posted on arXiv 5 Oct 2022.

## Builds on (most cited first, 6 of 6)

- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [A Tutorial on Kernel Density Estimation and Recent Advances](https://mlsanity.com/paper/1704.03924/) (2017)
- [Probabilistic forecast reconciliation under the Gaussian framework](https://mlsanity.com/paper/2103.11128/) (2021)
- [Cross-temporal forecast reconciliation: Optimal combination method and heuristic alternatives](https://mlsanity.com/paper/2006.08570/) (2020)
- [Probabilistic Reconciliation of Count Time Series](https://mlsanity.com/paper/2207.09322/) (2022)

## Built on by (most cited first, 1 of 1)

- [FoReco and FoRecoML: A Unified Toolbox for Forecast Reconciliation in R](https://mlsanity.com/paper/2604.27696/) (2026)

## Abstract (arXiv)

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.