arxiv: 2604.27696 · v1 · submitted 2026-04-30 · 📊 stat.CO · stat.AP· stat.ML

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FoReco and FoRecoML: A Unified Toolbox for Forecast Reconciliation in R

Daniele Girolimetto, Ines Wilms, Jeroen Rombouts, Yangzhuoran Fin Yang

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Pith reviewed 2026-05-07 04:53 UTC · model grok-4.3

classification 📊 stat.CO stat.APstat.ML

keywords forecast reconciliationR packagehierarchical time seriescross-sectional reconciliationtemporal reconciliationcross-temporal reconciliationmachine learninglinear reconciliation

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The pith

The R packages FoReco and FoRecoML supply a unified framework for forecast reconciliation that jointly handles cross-sectional, temporal, and cross-temporal cases with both linear and machine learning methods.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Forecast reconciliation adjusts predictions for multiple time series so they remain accurate while satisfying linear constraints, such as those found in hierarchical or grouped data structures. Until now, no single software solution offered full joint coverage of the three main reconciliation types together with both classical linear techniques and non-linear machine learning options. FoReco implements the linear approaches, while FoRecoML adds the machine learning variants, all inside one R environment that supplies sensible defaults for quick starts and full customization for advanced work. A sympathetic reader cares because this removes the need to cobble together separate tools or write custom code when working with constrained forecasts, letting practitioners apply coherent methods more readily. If the packages deliver on their design, reconciliation becomes a standard, low-friction step rather than an expert-only task.

Core claim

The paper presents FoReco and FoRecoML as the first comprehensive and unified R framework that implements classical and regression-based linear reconciliation together with machine-learning-based non-linear reconciliation, all applicable to cross-sectional, temporal, and cross-temporal frameworks. The packages are built for accessibility through default settings that allow immediate use by new practitioners, while retaining the flexibility expert users need to explore customized extensions of the underlying methods.

What carries the argument

The unified framework inside FoReco and FoRecoML that integrates classical linear, regression-based linear, and machine-learning non-linear reconciliation methods across the three structural frameworks.

If this is right

Practitioners can apply coherent forecasts to hierarchical series without switching packages or writing glue code between cross-sectional and temporal steps.
Researchers gain a single platform to compare linear and non-linear reconciliation performance on the same datasets and structures.
Default settings lower the barrier so that standard reconciliation becomes routine in applied forecasting workflows.
Expert users retain control to insert custom constraints or alternative base forecasts while staying inside the same environment.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The dual-package design could serve as a template for similar unified toolboxes in other languages such as Python.
Making machine-learning reconciliation available alongside linear methods invites direct empirical comparisons of when each class of method adds value.
Wider availability of cross-temporal reconciliation may encourage forecasters to model both cross-section and time dimensions simultaneously rather than sequentially.

Load-bearing premise

Existing software lacked any single tool that jointly covered cross-sectional, temporal, and cross-temporal reconciliation with both linear and non-linear methods, and the new packages correctly implement the referenced approaches while providing workable defaults.

What would settle it

A user running a single script that performs cross-temporal reconciliation first with a linear method and then with a machine-learning method, using only the packages' default functions and without writing additional bridging code, would confirm or refute whether the unified coverage actually works as described.

Figures

Figures reproduced from arXiv: 2604.27696 by Daniele Girolimetto, Ines Wilms, Jeroen Rombouts, Yangzhuoran Fin Yang.

**Figure 1.** Figure 1: Toy examples for cross-sectional, temporal and cross-temporal frameworks. view at source ↗

**Figure 2.** Figure 2: Reconciliation workflows. Panels (2a), (2b), and (2c) illustrates the main workflow of FoReco, summarizing the classical, regression-based, and probabilistic reconciliations. Panel (2d) presents the FoRecoML workflow view at source ↗

**Figure 3.** Figure 3: Italian energy load (×105 ): Base forecasts versus reconciled probabilistic forecasts from the Gaussian-based approach. R> reco_dist <- temvn(base = bf_italy, agg_order = 24, comb = "shr", + res = err_italy) The output is a vector of distributions view at source ↗

**Figure 4.** Figure 4: Italian energy load (×105 ): Base forecasts versus reconciled probabilistic forecasts from the sample-based approach. different cross-sectional hierarchy. Here we have 7 bidding zones and the total of Italy, so the row number is n = 8. For this simple cross-sectional hierarchy, the aggregation matrix agg_mat is just a single row of 7 ones. The entries in each row are the forecasts of different temporal hie… view at source ↗

read the original abstract

Forecast reconciliation has become key to improving the accuracy and coherence of forecasts for linearly constrained multiple time series, such as hierarchical and grouped series. Yet, comprehensive software that jointly covers cross-sectional, temporal, and cross-temporal reconciliation has so far been lacking. The R packages FoReco and FoRecoML address this gap by offering a comprehensive and unified framework. The packages respectively implement classical and regression-based linear reconciliation approaches, and non-linear approaches based on machine learning for cross-sectional, temporal and cross-temporal frameworks. Designed for accessibility and flexibility, these packages provide sensible default options that allow new users to apply reconciliation methods with minimal effort, while still giving expert users full control to explore state-of-the-art extensions through customized settings. With this dual focus, FoReco and FoRecoML are versatile tools for practitioners and researchers working on forecast reconciliation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

FoReco and FoRecoML consolidate existing reconciliation techniques into unified R tools, offering practical value without new methodological contributions.

read the letter

FoReco and FoRecoML are R packages that consolidate classical, regression-based, and machine learning forecast reconciliation techniques into a single accessible framework for cross-sectional, temporal, and cross-temporal hierarchies. The paper does well in explaining the design choices that make the tools usable for both beginners and experts. By offering sensible defaults alongside full customization options, it lowers the barrier for applying reconciliation methods that improve forecast coherence in constrained time series. This is particularly relevant for fields like supply chain and economics where hierarchical forecasts are common. The packages build directly on published methods, so the core ideas are grounded in existing literature rather than untested innovations. The soft spots are minor but worth noting. Since this is a software paper, its strength depends on the quality of the code and documentation, which the abstract does not demonstrate with examples or tests. The claim that comprehensive joint support was lacking before needs verification against other R packages in the area, though the authors position it as filling that gap. No major inconsistencies appear in the description, and the argument is straightforward. This paper is for applied statisticians and forecasters working in R who want a convenient way to implement reconciliation without switching between multiple tools. A reader interested in practical implementation would find value in the unified interface and the dual focus on accessibility and flexibility. Someone seeking theoretical advances in reconciliation methods would get less out of it. I recommend engaging with the work through peer review. Software contributions that make established techniques easier to use can be worthwhile, and a referee could provide feedback on usability, completeness of the feature set, and any potential improvements to the package design.

Referee Report

1 major / 0 minor

Summary. The manuscript introduces the R packages FoReco and FoRecoML as a unified toolbox for forecast reconciliation. FoReco implements classical and regression-based linear reconciliation methods, while FoRecoML adds non-linear machine-learning approaches; both cover cross-sectional, temporal, and cross-temporal frameworks. The packages are positioned as accessible via sensible defaults yet extensible for expert users through customization options, addressing a claimed gap in existing software.

Significance. If the packages function as described and are made available with working implementations, the work is significant for computational statistics and forecasting practice. Forecast reconciliation improves coherence and accuracy in hierarchical time series, and a single R framework spanning linear and non-linear methods across the three reconciliation settings can reduce implementation barriers and support reproducible research in demand planning, energy, and related domains.

major comments (1)

The manuscript describes the intended functionality and design goals but contains no code snippets, usage examples, or empirical benchmarks (e.g., reconciliation error metrics on standard hierarchical datasets). This absence is load-bearing for the central claim that the packages supply a 'comprehensive and unified framework' that is both accessible and correct; without demonstrations, readers cannot assess usability or implementation fidelity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive feedback and recommendation. We address the single major comment below and will revise the manuscript accordingly to strengthen the presentation of the packages.

read point-by-point responses

Referee: The manuscript describes the intended functionality and design goals but contains no code snippets, usage examples, or empirical benchmarks (e.g., reconciliation error metrics on standard hierarchical datasets). This absence is load-bearing for the central claim that the packages supply a 'comprehensive and unified framework' that is both accessible and correct; without demonstrations, readers cannot assess usability or implementation fidelity.

Authors: We agree that the current manuscript would be strengthened by the addition of concrete demonstrations. While the packages themselves include extensive documentation, vignettes, and example datasets, the manuscript text focuses primarily on design and functionality. In the revised version we will insert a new section containing short, self-contained R code snippets that illustrate the main reconciliation functions (e.g., recoin, recoin_ml) for cross-sectional, temporal, and cross-temporal hierarchies under both linear and non-linear settings. We will also add a brief empirical illustration on a publicly available hierarchical dataset (such as the Australian tourism or M5 retail data), reporting standard accuracy metrics (RMSE, MASE) before and after reconciliation to allow readers to verify usability and implementation fidelity. revision: yes

Circularity Check

0 steps flagged

No circularity: software description paper with no derivations or self-referential predictions

full rationale

The paper is a description of two R packages (FoReco and FoRecoML) that implement existing forecast reconciliation methods from prior literature. It makes no mathematical derivations, first-principles claims, fitted parameters, or predictions that could reduce to quantities defined within the paper itself. The central claim is simply that the packages provide a unified, accessible framework covering cross-sectional, temporal, and cross-temporal reconciliation, with defaults and customization options. This is self-contained as a factual statement about implemented software functionality and does not rely on any internal equations or self-citation chains for its validity. References to prior work on reconciliation methods are external and independent. No load-bearing steps reduce by construction to the paper's own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is a software-description paper. No new mathematical derivations, free parameters, axioms, or invented entities are introduced. All referenced reconciliation approaches are drawn from prior literature.

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discussion (0)

Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages

[1]

Improving Cross-temporal Fore- casts Reconciliation Accuracy and Utility in Energy Market

Abolghasemi M, Girolimetto D, Di Fonzo T (2025). “Improving Cross-temporal Fore- casts Reconciliation Accuracy and Utility in Energy Market.”Applied Energy,394, 126053.doi:10.1016/j.apenergy.2025.126053. URLhttp://dx.doi.org/10.1016/ j.apenergy.2025.126053. AndoS,XiaoM(2023). “High-DimensionalCovarianceMatrixEstimation: ShrinkageToward a Diagonal Target.”...

work page doi:10.1016/j.apenergy.2025.126053 2025
[2]

Understanding Forecast Reconciliation

Sequential, Iterative, and Optimal approaches.”Statistical Methods & Applications,in press.doi:10.1007/s10260-025-00822-z. Daniele Girolimetto, Jeroen Rombouts, Ines Wilms, Yangzhuoran Fin Yang29 Girolimetto D, Di Fonzo T (2025).FoReco: Forecast Reconciliation.doi:10.32614/CRAN. package.FoReco.Rpackage version 1.2.0, URLhttps://CRAN.R-project.org/package=...

work page doi:10.1007/s10260-025-00822-z 2025