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arxiv: 2604.27696 · v2 · pith:FCXHZXXTnew · submitted 2026-04-30 · 📊 stat.CO · stat.AP· stat.ML

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

Daniele Girolimetto , Jeroen Rombouts , Ines Wilms , Yangzhuoran Fin Yang This is my paper

Pith reviewed 2026-07-01 08:02 UTC · model grok-4.3

classification 📊 stat.CO stat.APstat.ML
keywords forecast reconciliationR packageshierarchical time seriestemporal reconciliationcross-temporal reconciliationmachine learninglinear constraintsforecast coherence
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The pith

The R packages FoReco and FoRecoML provide a unified framework for linear and non-linear forecast reconciliation across cross-sectional, temporal, and cross-temporal structures.

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

Forecast reconciliation improves accuracy and coherence for forecasts of multiple time series that must obey linear constraints, such as hierarchical or grouped series. No single software had previously covered all three reconciliation types together. FoReco supplies classical and regression-based linear methods. FoRecoML adds machine learning approaches for non-linear reconciliation. The packages supply defaults for quick use while permitting full customization for advanced work.

Core claim

The paper introduces FoReco and FoRecoML as R packages that together supply a unified toolbox implementing classical linear, regression-based linear, and machine learning non-linear reconciliation for cross-sectional, temporal, and cross-temporal frameworks, addressing the prior absence of comprehensive joint coverage.

What carries the argument

The unified R toolbox in FoReco and FoRecoML that combines linear reconciliation methods with machine learning non-linear methods to enforce coherence in constrained multiple time series forecasts.

If this is right

  • Forecasts for hierarchical and grouped series gain both higher accuracy and guaranteed coherence.
  • Practitioners can switch between linear and non-linear methods inside the same software environment.
  • New users apply methods immediately via defaults while experts retain control over extensions.
  • All three reconciliation frameworks become available without switching between separate tools.

Where Pith is reading between the lines

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

  • The packages could reduce the barrier to using reconciliation in routine forecasting workflows.
  • Integration points with other R forecasting libraries might emerge to broaden data handling.
  • Non-linear ML reconciliation could be examined on problems where linear constraints are known to be insufficient.

Load-bearing premise

Existing separate tools leave a meaningful gap that one new unified R toolbox can fill without adding implementation errors or performance problems.

What would settle it

A side-by-side test showing that existing fragmented packages already allow users to perform cross-sectional, temporal, and cross-temporal reconciliation together without gaps or extra effort would disprove the need for these packages.

Figures

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

Figure 1
Figure 1. Figure 1: Toy examples for cross-sectional, temporal and cross-temporal frameworks. view at source ↗
Figure 2
Figure 2. Figure 2: Reconciliation workflows. Panels (2a), (2b), and (2c) illustrates the main work￾flow of FoReco, summarizing the classical, regression-based, and probabilistic reconciliations. Panel (2d) presents the FoRecoML workflow view at source ↗
Figure 3
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. 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.

Referee Report

0 major / 3 minor

Summary. The manuscript describes the R packages FoReco and FoRecoML as a unified toolbox for forecast reconciliation. FoReco implements classical and regression-based linear reconciliation methods, while FoRecoML implements non-linear machine learning approaches; both cover cross-sectional, temporal, and cross-temporal frameworks. The packages emphasize accessibility via sensible defaults for new users alongside full customization options for experts.

Significance. If the packages deliver the claimed coverage and usability without introducing unaddressed implementation issues, the work would address a genuine software gap in the field by consolidating fragmented tools into a single flexible framework. The dual focus on defaults and customization is a concrete strength that could broaden adoption of reconciliation methods among both practitioners and researchers.

minor comments (3)
  1. The manuscript would benefit from an explicit comparison table (perhaps in a dedicated section on related software) listing which specific methods from the literature are newly unified versus already available in packages such as hts or thief.
  2. Add at least one reproducible code example in the main text or supplementary material demonstrating a cross-temporal reconciliation workflow with both default and customized settings to illustrate the accessibility claims.
  3. Ensure all methodological references underlying the implemented linear and ML reconciliation procedures are cited in the text, particularly for the regression-based and non-linear approaches.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary of the manuscript, recognition of the packages' scope and usability focus, and recommendation for minor revision. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity; software description paper

full rationale

The manuscript is a description of two R packages (FoReco and FoRecoML) that implement existing reconciliation methods for hierarchical time series. No derivation chain, first-principles results, fitted predictions, or uniqueness theorems appear in the provided abstract or scope. The central claim is simply that the packages supply a unified, accessible implementation covering cross-sectional, temporal, and cross-temporal cases; this is an engineering contribution whose validity is external (code correctness, benchmarks) rather than internally self-referential. No load-bearing self-citations, ansatzes, or renamings of known results are present. This matches the default expectation for non-derivational papers and receives the lowest circularity score.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only input contains no mathematical content, free parameters, axioms, or invented entities.

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