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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

This paper addresses a common problem with hierarchical time series. Time series analysis demands the series for a model to be the sum of multiple series at corresponding sub-levels. Hierarchical Time Series presents a two-fold problem.…

Applications · Statistics 2022-12-27 Seema Sangari , Xinyan Zhang

We propose a novel approach to the problem of clustering hierarchically aggregated time-series data, which has remained an understudied problem though it has several commercial applications. We first group time series at each aggregated…

Machine Learning · Computer Science 2022-05-30 Xing Han , Tongzheng Ren , Jing Hu , Joydeep Ghosh , Nhat Ho

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

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

Existing hierarchical forecasting techniques scale poorly when the number of time series increases. We propose to learn a coherent forecast for millions of time series with a single bottom-level forecast model by using a sparse loss…

Machine Learning · Computer Science 2024-02-27 Olivier Sprangers , Wander Wadman , Sebastian Schelter , Maarten de Rijke

The practical importance of coherent forecasts in hierarchical forecasting has inspired many studies on forecast reconciliation. Under this approach, so-called base forecasts are produced for every series in the hierarchy and are…

Methodology · Statistics 2022-04-21 Bohan Zhang , Yanfei Kang , Anastasios Panagiotelis , Feng Li

We present a novel approach for reconciling hierarchical forecasts, based on Bayes rule. We define a prior distribution for the bottom time series of the hierarchy, based on the bottom base forecasts. Then we update their distribution via…

Applications · Statistics 2021-06-07 Giorgio Corani , Dario Azzimonti , João P. S. C. Augusto , Marco Zaffalon

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

Relationships among time series can be exploited as inductive biases in learning effective forecasting models. In hierarchical time series, relationships among subsets of sequences induce hard constraints (hierarchical inductive biases) on…

Machine Learning · Computer Science 2024-08-22 Andrea Cini , Danilo Mandic , Cesare Alippi

In recent years, machine learning has established itself as a powerful tool for high-resolution weather forecasting. While most current machine learning models focus on deterministic forecasts, accurately capturing the uncertainty in the…

Machine Learning · Computer Science 2024-10-29 Joel Oskarsson , Tomas Landelius , Marc Peter Deisenroth , Fredrik Lindsten

Aggregation constraints, arising from geographical or sectoral division, frequently emerge in a large set of time series. Coherent forecasts of these constrained series are anticipated to conform to their hierarchical structure organized by…

Applications · Statistics 2026-02-27 Zhichao Wang , Shanshan Wang , Wei Cao , Fei Yang

We focus on solving the univariate times series point forecasting problem using deep learning. We propose a deep neural architecture based on backward and forward residual links and a very deep stack of fully-connected layers. The…

Machine Learning · Computer Science 2020-02-24 Boris N. Oreshkin , Dmitri Carpov , Nicolas Chapados , Yoshua Bengio

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…

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

This paper addresses the mid-term electricity load forecasting problem. Solving this problem is necessary for power system operation and planning as well as for negotiating forward contracts in deregulated energy markets. We show that our…

Machine Learning · Computer Science 2021-04-06 Boris N. Oreshkin , Grzegorz Dudek , Paweł Pełka , Ekaterina Turkina

Time series forecasting plays an increasingly important role in modern business decisions. In today's data-rich environment, people often aim to choose the optimal forecasting model for their data. However, identifying the optimal model…

Applications · Statistics 2021-12-17 Xixi Li , Fotios Petropoulos , Yanfei Kang

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

Time series forecasting serves as an essential tool for many real-world applications, supporting tasks such as resource optimization and decision-making. Despite significant architectural advancements, most modern models still treat…

Machine Learning · Computer Science 2026-05-12 Sheng Pan , Ming Jin , Bo Du , Shirui Pan

Large-scale classification of data where classes are structurally organized in a hierarchy is an important area of research. Top-down approaches that exploit the hierarchy during the learning and prediction phase are efficient for large…

Machine Learning · Computer Science 2017-06-06 Azad Naik , Huzefa Rangwala