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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

Time series often appear in an additive hierarchical structure. In such cases, time series on higher levels are the sums of their subordinate time series. This hierarchical structure places a natural constraint on forecasts. However,…

Methodology · Statistics 2025-03-20 Louis Steinmeister , Markus Pauly

We introduce a dynamic approach to probabilistic forecast reconciliation at scale. Our model differs from the existing literature in this area in several important ways. Firstly we explicitly allow the weights allocated to the base…

Methodology · Statistics 2024-09-20 Ross Hollyman , Fotios Petropoulos , Michael E. Tipping

Forecast reconciliation is a post-forecasting process aimed to improve the quality of the base forecasts for a system of hierarchical/grouped time series (Hyndman et al., 2011). Contemporaneous (cross-sectional) and temporal hierarchies…

Methodology · Statistics 2023-10-30 Tommaso Di Fonzo , Daniele Girolimetto

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

Forecast reconciliation is a post-forecasting process that involves transforming a set of incoherent forecasts into coherent forecasts which satisfy a given set of linear constraints for a multivariate time series. In this paper we extend…

Methodology · Statistics 2023-12-25 Daniele Girolimetto , George Athanasopoulos , Tommaso Di Fonzo , Rob J Hyndman

When forecasting time series with a hierarchical structure, the existing state of the art is to forecast each time series independently, and, in a post-treatment step, to reconcile the time series in a way that respects the hierarchy…

Machine Learning · Statistics 2019-06-26 Konstantin Mishchenko , Mallory Montgomery , Federico Vaggi

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

In machine learning, effective modeling requires a holistic consideration of how to encode inputs, make predictions (i.e., decoding), and train the model. However, in time-series forecasting, prior work has predominantly focused on encoder…

Machine Learning · Computer Science 2025-12-30 Jaebin Lee , Hankook Lee

In hierarchical forecasting, the process of forecast reconciliation transforms a set of "base" or "raw" forecasts, which do not satisfy the hierarchical aggregation constraints in the real data, into a set of "coherent" forecasts, which do…

Methodology · Statistics 2026-05-29 Minh Nguyen , Farshid Vahid , Shanika L Wickramasuriya

Forecast reconciliation is the post-forecasting process aimed to revise a set of incoherent base forecasts into coherent forecasts in line with given data structures. Most of the point and probabilistic regression-based forecast…

Methodology · Statistics 2023-12-25 Daniele Girolimetto , Tommaso Di Fonzo

This paper presents a formal framework and proposes algorithms to extend forecast reconciliation to discrete-valued data to extend forecast reconciliation to discrete-valued data, including low counts. A novel method is introduced based on…

Methodology · Statistics 2024-04-16 Bohan Zhang , Anastasios Panagiotelis , Yanfei Kang

Ads demand forecasting for Walmart's ad products plays a critical role in enabling effective resource planning, allocation, and management of ads performance. In this paper, we introduce a comprehensive demand forecasting system that…

Machine Learning · Computer Science 2024-12-20 Zhengchao Yang , Mithun Ghosh , Anish Saha , Dong Xu , Konstantin Shmakov , Kuang-chih Lee

Hierarchical time-series forecasting is essential for demand prediction across various industries. While machine learning models have obtained significant accuracy and scalability on such forecasting tasks, the interpretability of their…

Machine Learning · Computer Science 2026-03-09 Harshavardhan Kamarthi , Shangqing Xu , Xinjie Tong , Xingyu Zhou , James Peters , Joseph Czyzyk , B. Aditya Prakash

As the popularity of hierarchical point forecast reconciliation methods increases, there is a growing interest in probabilistic forecast reconciliation. Many studies have utilized machine learning or deep learning techniques to implement…

Artificial Intelligence · Computer Science 2023-11-22 Guanyu Zhang , Feng Li , Yanfei Kang

The problem of combining multiple forecasts of related quantities that obey expected equality and additivity constraints, often referred to a hierarchical forecast reconciliation, is naturally stated as a simple optimization problem. In…

Methodology · Statistics 2026-02-10 Tianyu Wang , Matthew C. Johnson , Steven Klee , Matthew L. Malloy

Getting a robust time-series clustering with best choice of distance measure and appropriate representation is always a challenge. We propose a novel mechanism to identify the clusters combining learned compact representation of…

Machine Learning · Computer Science 2021-01-12 Soma Bandyopadhyay , Anish Datta , Arpan Pal

In forecasting multiple time series, accounting for the individual features of each sequence can be challenging. To address this, modern deep learning methods for time series analysis combine a shared (global) model with local layers,…

Machine Learning · Computer Science 2025-02-14 Luca Butera , Giovanni De Felice , Andrea Cini , Cesare Alippi

Nowadays, time series forecasting is predominantly approached through the end-to-end training of deep learning architectures using error-based objectives. While this is effective at minimizing average loss, it encourages the encoder to…

Machine Learning · Computer Science 2026-03-26 Jiacheng Wang , Liang Fan , Baihua Li , Luyan Zhang

Learned time-series models, whether continuous or discrete, are widely used for forecasting the states of dynamical systems but suffer from error accumulation in multi-step forecasts. To address this issue, we propose a Predictor-Corrector…

Machine Learning · Computer Science 2026-05-11 Muhammad Bilal Shahid , Zhanhong Jiang , Prajwal Koirala , Soumik Sarkar , Cody Fleming