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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

In this paper, we propose a machine learning approach for forecasting hierarchical time series. When dealing with hierarchical time series, apart from generating accurate forecasts, one needs to select a suitable method for producing…

Machine Learning · Computer Science 2021-07-12 Paolo Mancuso , Veronica Piccialli , Antonio M. Sudoso

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

We address the problem of uncertainty quantification in time series forecasting by exploiting observations at correlated sequences. Relational deep learning methods leveraging graph representations are among the most effective tools for…

Machine Learning · Computer Science 2025-06-09 Andrea Cini , Alexander Jenkins , Danilo Mandic , Cesare Alippi , Filippo Maria Bianchi

Probabilistic hierarchical time-series forecasting is an important variant of time-series forecasting, where the goal is to model and forecast multivariate time-series that have underlying hierarchical relations. Most methods focus on point…

Machine Learning · Computer Science 2023-10-20 Harshavardhan Kamarthi , Lingkai Kong , Alexander Rodríguez , Chao Zhang , B. Aditya Prakash

Probabilistic hierarchical time-series forecasting is an important variant of time-series forecasting, where the goal is to model and forecast multivariate time-series that have underlying hierarchical relations. Most methods focus on point…

Machine Learning · Computer Science 2023-10-20 Harshavardhan Kamarthi , Lingkai Kong , Alexander Rodríguez , Chao Zhang , B. Aditya Prakash

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

Time series forecasting remains a critical challenge across numerous domains, yet the effectiveness of complex models often varies unpredictably across datasets. Recent studies highlight the surprising competitiveness of simple linear…

Machine Learning · Computer Science 2026-05-14 Zheng Wang , Kaixuan Zhang , Wanfang Chen , Xiaonan Lu , Longyuan Li , Tobias Schlagenhauf

Hierarchical forecasting with reconciliation requires forecasting values of a hierarchy (e.g.~customer demand in a state and district), such that forecast values are linked (e.g.~ district forecasts should add up to the state forecast).…

Machine Learning · Computer Science 2025-05-09 Charupriya Sharma , Iñaki Estella Aguerri , Daniel Guimarans

Many sectors nowadays require accurate and coherent predictions across their organization to effectively operate. Otherwise, decision-makers would be planning using disparate views of the future, resulting in inconsistent decisions across…

Machine Learning · Computer Science 2023-02-09 Julien Leprince , Waqas Khan , Henrik Madsen , Jan Kloppenborg Møller , Wim Zeiler

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

Rule-based systems must solve complex matching problems within tight time constraints to be effective in real-time applications, such as planning and reactive control for AI agents, as well as low-latency relational database querying.…

Artificial Intelligence · Computer Science 2025-11-19 Daniel Weitekamp

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

We introduce a framework to dynamically combine heterogeneous models called \texttt{DYCHEM}, which forecasts a set of time series that are related through an aggregation hierarchy. Different types of forecasting models can be employed as…

Machine Learning · Computer Science 2023-01-18 Xing Han , Jing Hu , Joydeep Ghosh

To learn and reason in the presence of uncertainty, the brain must be capable of imposing some form of regularization. Here we suggest, through theoretical and computational arguments, that the combination of noise with synchronization…

Neurons and Cognition · Quantitative Biology 2013-12-06 Jake Bouvrie , Jean-Jacques Slotine

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

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…

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

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

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
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