Coherent Hierarchical Forecasting for Proportion and Discrete Time Series
Abstract
Hierarchical and grouped time series arise when a multivariate time series is forced to satisfy a set of aggregation constraints, motivating forecast reconciliation methods that ensure coherent forecasts of such hierarchical structures. Many real-world applications involve discrete or bounded supports, introducing additional challenges that are not addressed Gaussian-based reconciliation methods. We develop a post-hoc hierarchical forecasting approach to construct coherent forecast hierarchies for discrete and bounded time series. The method constructs coherent forecasts by convolution and exponential tilting, preserving the distributional properties and the underlying support throughout the hierarchy. We evaluate the proposed approach against state-of-the-art reconciliation methods for both discrete and continuous settings, demonstrating strong performance across a range of experiments. Through simulation studies and empirical applications in epidemiological and demographic data, we show that the method provides reliable and coherent distributional forecasts in challenging scenarios.
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BibTeX
@misc{comiskey2026coherent,
title = {{Coherent Hierarchical Forecasting for Proportion and Discrete Time Series}},
author = {Hannah Comiskey},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17918},
eprint = {2609.17918},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17918},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Coherent Hierarchical Forecasting for Proportion and Discrete Time Series
AU - Hannah Comiskey
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17918
UR - https://arxiv.org/abs/2609.17918
AB - Hierarchical and grouped time series arise when a multivariate time series is forced to satisfy a set of aggregation constraints, motivating forecast reconciliation methods that ensure coherent forecasts of such hierarchical structures. Many real-world applications involve discrete or bounded supports, introducing additional challenges that are not addressed Gaussian-based reconciliation methods. We develop a post-hoc hierarchical forecasting approach to construct coherent forecast hierarchies for discrete and bounded time series. The method constructs coherent forecasts by convolution and exponential tilting, preserving the distributional properties and the underlying support throughout the hierarchy. We evaluate the proposed approach against state-of-the-art reconciliation methods for both discrete and continuous settings, demonstrating strong performance across a range of experiments. Through simulation studies and empirical applications in epidemiological and demographic data, we show that the method provides reliable and coherent distributional forecasts in challenging scenarios.
ER -