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This paper focuses on forecasting hierarchical time-series data, where each higher-level observation equals the sum of its corresponding lower-level time series. In such contexts, the forecast values should be coherent, meaning that the…

Machine Learning · Computer Science 2026-02-06 Shuhei Aikawa , Aru Suzuki , Kei Yoshitake , Kanata Teshigawara , Akira Iwabuchi , Ken Kobayashi , Kazuhide Nakata

Hierarchical forecasting methods have been widely used to support aligned decision-making by providing coherent forecasts at different aggregation levels. Traditional hierarchical forecasting approaches, such as the bottom-up and top-down…

Machine Learning · Computer Science 2020-06-04 Evangelos Spiliotis , Mahdi Abolghasemi , Rob J Hyndman , Fotios Petropoulos , Vassilios Assimakopoulos

Model selection has been proven an effective strategy for improving accuracy in time series forecasting applications. However, when dealing with hierarchical time series, apart from selecting the most appropriate forecasting model,…

Machine Learning · Computer Science 2020-10-30 Mahdi Abolghasemi , Rob J Hyndman , Evangelos Spiliotis , Christoph Bergmeir

This paper discusses the prediction of hierarchical time series, where each upper-level time series is calculated by summing appropriate lower-level time series. Forecasts for such hierarchical time series should be coherent, meaning that…

Machine Learning · Computer Science 2021-01-27 Tomokaze Shiratori , Ken Kobayashi , Yuichi Takano

Hierarchical forecasting is a key problem in many practical multivariate forecasting applications - the goal is to simultaneously predict a large number of correlated time series that are arranged in a pre-specified aggregation hierarchy.…

Machine Learning · Computer Science 2021-10-13 Biswajit Paria , Rajat Sen , Amr Ahmed , Abhimanyu Das

In numerous applications, it is required to produce forecasts for multiple time-series at different hierarchy levels. An obvious example is given by the supply chain in which demand forecasting may be needed at a store, city, or country…

Machine Learning · Computer Science 2021-01-06 Davide Burba , Trista Chen

We examine the problem of making reconciled forecasts of large collections of related time series through a behavioural/Bayesian lens. Our approach explicitly acknowledges and exploits the 'connectedness' of the series in terms of…

Methodology · Statistics 2022-10-03 Ross Hollyman , Fotios Petropoulos , Michael E. Tipping

We encounter time series data in many domains such as finance, physics, business, and weather. One of the main tasks of time series analysis, one that helps to take informed decisions under uncertainty, is forecasting. Time series are often…

Artificial Intelligence · Computer Science 2023-08-29 Gal Elgavish

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…

Machine Learning · Statistics 2023-10-13 Lorenzo Zambon , Dario Azzimonti , Giorgio Corani

Forecast reconciliation has attracted significant research interest in recent years, with most studies taking the hierarchy of time series as given. We extend existing work that uses time series clustering to construct hierarchies, with the…

Methodology · Statistics 2024-09-10 Bohan Zhang , Anastasios Panagiotelis , Han Li

Some time series can be hierarchically organized into levels based on certain characteristics, such as geography or other attributes of interest. These series are referred to as hierarchical time series. Typically, forecasts are generated…

Optimal decision-making compels us to anticipate the future at different horizons. However, in many domains connecting together predictions from multiple time horizons and abstractions levels across their organization becomes all the more…

Machine Learning · Computer Science 2023-07-06 Julien Leprince , Henrik Madsen , Jan Kloppenborg Møller , Wim Zeiler

A novel framework for hierarchical forecast updating is presented, addressing a critical gap in the forecasting literature. By assuming a temporal hierarchy structure, the innovative approach extends hierarchical forecast reconciliation to…

Methodology · Statistics 2024-11-05 Lukas Neubauer , Peter Filzmoser

Multivariate time series forecasting with hierarchical structure is widely used in real-world applications, e.g., sales predictions for the geographical hierarchy formed by cities, states, and countries. The hierarchical time series (HTS)…

Machine Learning · Computer Science 2023-10-10 Fan Zhou , Chen Pan , Lintao Ma , Yu Liu , Shiyu Wang , James Zhang , Xinxin Zhu , Xuanwei Hu , Yunhua Hu , Yangfei Zheng , Lei Lei , Yun Hu

Large collections of time series data are often organized into hierarchies with different levels of aggregation; examples include product and geographical groupings. Probabilistic coherent forecasting is tasked to produce forecasts…

Multivariate time series forecasting with hierarchical structure is pervasive in real-world applications, demanding not only predicting each level of the hierarchy, but also reconciling all forecasts to ensure coherency, i.e., the forecasts…

Machine Learning · Computer Science 2025-03-04 Shiyu Wang , Fan Zhou , Yinbo Sun , Lintao Ma , James Zhang , Yangfei Zheng

Platform businesses operate on a digital core and their decision making requires high-dimensional accurate forecast streams at different levels of cross-sectional (e.g., geographical regions) and temporal aggregation (e.g., minutes to…

Econometrics · Economics 2024-06-03 Jeroen Rombouts , Marie Ternes , Ines Wilms

An important task for any large-scale organization is to prepare forecasts of key performance metrics. Often these organizations are structured in a hierarchical manner and for operational reasons, projections of these metrics may have been…

Applications · Statistics 2017-11-15 Julie Novak , Scott McGarvie , Beatriz Etchegaray Garcia

Many real-life applications involve simultaneously forecasting multiple time series that are hierarchically related via aggregation or disaggregation operations. For instance, commercial organizations often want to forecast inventories…

Machine Learning · Computer Science 2021-02-26 Xing Han , Sambarta Dasgupta , Joydeep Ghosh

The rapid development of time series forecasting research has brought many deep learning-based modules in this field. However, despite the increasing amount of new forecasting architectures, it is still unclear if we have leveraged the full…

Machine Learning · Computer Science 2025-10-24 Difan Deng , Marius Lindauer
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