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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

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

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

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

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

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 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

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

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

Methods for forecasting time series adhering to linear constraints have seen notable development in recent years, especially with the advent of forecast reconciliation. This paper extends forecast reconciliation to the open question of…

Methodology · Statistics 2025-10-27 Daniele Girolimetto , Anastasios Panagiotelis , Tommaso Di Fonzo , Han Li

Forecast reconciliation adjusts independently generated forecasts so that they satisfy some known constraints. While probabilistic forecast reconciliation is well established for linear constraints, some practical forecasting problems…

Methodology · Statistics 2026-04-30 Anubhab Biswas , Lorenzo Zambon , Lorenzo Nespoli , Giorgio Corani

Reconciliation enforces coherence between hierarchical forecasts, in order to satisfy a set of linear constraints. While most works focus on the reconciliation of the point forecasts, we consider probabilistic reconciliation and we analyze…

Applications · Statistics 2024-02-15 Lorenzo Zambon , Arianna Agosto , Paolo Giudici , Giorgio Corani

In recent works by Yang et al. (2017a,b), and Yagli et al. (2019), geographical, temporal, and sequential deterministic reconciliation of hierarchical photovoltaic (PV) power generation have been considered for a simulated PV dataset in…

Applications · Statistics 2022-09-16 Tommaso Di Fonzo , Daniele Girolimetto

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

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 combinations have flourished remarkably in the forecasting community and, in recent years, have become part of the mainstream of forecasting research and activities. Combining multiple forecasts produced from single (target) series…

Methodology · Statistics 2022-09-26 Xiaoqian Wang , Rob J Hyndman , Feng Li , Yanfei Kang

Forecast reconciliation of multivariate time series is the process of mapping a set of incoherent forecasts into coherent forecasts to satisfy a given set of linear constraints. Commonly used projection matrix based approaches for point…

Methodology · Statistics 2021-03-23 Shanika L Wickramasuriya

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 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

It is often reported in forecast combination literature that a simple average of candidate forecasts is more robust than sophisticated combining methods. This phenomenon is usually referred to as the "forecast combination puzzle". Motivated…

Methodology · Statistics 2015-05-05 Wei Qian , Craig A. Rolling , Gang Cheng , Yuhong Yang
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