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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

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

Time series forecasting occurs in a range of financial applications providing essential decision-making support to investors, regulatory institutions, and analysts. Unlike multivariate time series from other domains, stock time series…

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

This paper presents a practical architecture for after-sales demand forecasting and monitoring that unifies a revenue- and cluster-aware ensemble of statistical, machine-learning, and deep-learning models with a role-driven analytics layer…

Artificial Intelligence · Computer Science 2025-10-02 Saravanan Venkatachalam

Cross-temporal forecast reconciliation aims to ensure consistency across forecasts made at different temporal and cross-sectional levels. We explore the relationships between sequential, iterative, and optimal combination approaches, and…

Methodology · Statistics 2024-10-28 Daniele Girolimetto , Tommaso Di Fonzo

In a recent paper, while elucidating the links between forecast combination and cross-sectional forecast reconciliation, Hollyman et al. (2021) have proposed a forecast combination-based approach to the reconciliation of a simple hierarchy.…

Applications · Statistics 2021-06-11 Tommaso Di Fonzo , Daniele Girolimetto

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

Large collections of time series data are commonly organized into structures with different levels of aggregation; examples include product and geographical groupings. It is often important to ensure that the forecasts are coherent so that…

Linearly constrained multiple time series may be encountered in many practical contexts, such as the National Accounts (e.g., GDP disaggregated by Income, Expenditure and Output), and multilevel frameworks where the variables are organized…

Methodology · Statistics 2024-12-05 Daniele Girolimetto , Tommaso Di Fonzo

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

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

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

Seasonal time series Forecasting remains a challenging problem due to the long-term dependency from seasonality. In this paper, we propose a two-stage framework to forecast univariate seasonal time series. The first stage explicitly learns…

Machine Learning · Computer Science 2021-06-08 Qingyang Xu , Qingsong Wen , Liang Sun

Generating accurate and reliable sales forecasts is crucial in the E-commerce business. The current state-of-the-art techniques are typically univariate methods, which produce forecasts considering only the historical sales data of a single…

Machine Learning · Computer Science 2019-08-13 Kasun Bandara , Peibei Shi , Christoph Bergmeir , Hansika Hewamalage , Quoc Tran , Brian Seaman

Hierarchical forecasting (HF) is needed in many situations in the supply chain (SC) because managers often need different levels of forecasts at different levels of SC to make a decision. Top-Down (TD), Bottom-Up (BU) and Optimal…

Machine Learning · Computer Science 2019-12-03 Mahdi Abolghasemi , Rob J Hyndman , Garth Tarr , Christoph Bergmeir

This research article suggests that there are significant benefits in exposing demand planners to forecasting methods using matrix completion techniques. This study aims to contribute to a better understanding of the field of forecasting…

Applications · Statistics 2020-09-10 Rodrigo Rivera-Castro , Ivan Nazarov , Evgeny Burnaev

The features in many prediction models naturally take the form of a hierarchy. The lower levels represent individuals or events. These units group naturally into locations and intervals or other aggregates, often at multiple levels. Levels…

Applications · Statistics 2023-07-03 John Mark Agosta , Mario Inchiosa

Time series forecasting presents significant challenges due to the complex temporal dependencies at multiple time scales. This paper introduces ScatterFusion, a novel framework that synergistically integrates scattering transforms with…

Machine Learning · Computer Science 2026-01-29 Wei Li