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

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

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

0 comments

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: 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 package existing reconciliation methods into one R toolbox, which fills a practical gap for users but adds no new theory or empirical results.

read the letter

The key point is that this paper presents two R packages, FoReco and FoRecoML, that implement a range of forecast reconciliation techniques in one place. They cover linear methods like classical and regression-based, plus non-linear machine learning ones, across cross-sectional, temporal, and cross-temporal settings.

What stands out is the effort to make these tools accessible. The packages come with sensible defaults so beginners can use them easily, while allowing experts to tweak settings for more advanced work. This dual approach is a solid design choice for a toolbox.

The unification itself is the main novelty here. Before, users had to hunt for separate tools for different types of reconciliation, so bringing them together under consistent interfaces is a practical step forward.

That said, the paper is describing software rather than proving new results. The claims rest on the packages working as advertised, but without details on validation or benchmarks in the provided description, it's hard to gauge implementation quality. Any issues with numerical stability or edge cases would need checking in the actual code.

This work is for people doing hierarchical forecasting in R who want an all-in-one solution. Readers interested in applied forecasting tools would get value from it.

It deserves a serious referee because the gap it claims to fill is real for practitioners, even if the underlying methods are established. I would send it to peer review.

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)

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.
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.
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.

pith-pipeline@v0.9.1-grok · 5685 in / 936 out tokens · 23643 ms · 2026-07-01T08:02:06.316766+00:00 · methodology

Review history (2 revisions) →

discussion (0)

Reference graph

Works this paper leans on

14 extracted references · 14 canonical work pages · 1 internal anchor

[1]

European Journal of Cance r �� , 1–2 (2023) https://doi.org/10.1016/J.EJCA.2022.12.008

Rijken, A., Erning, F.N., Rovers, K.P., Lemmens, V.E.P.P., Hingh, I.H.J.T .: On the origin of peritoneal metastases. European Journal of Cance r �� , 1–2 (2023) https://doi.org/10.1016/J.EJCA.2022.12.008

work page doi:10.1016/j.ejca.2022.12.008 2023
[2]

Pleura and Peritoneum �(2), 51–61 (2022) https://doi.org/10.1515/pp-2021-0152

Noiret, B., Piessen, G., Eveno, C.: Update of randomized controlle d tri- als evaluating cytoreductive surgery (CRS) and hyperthermic intr aperitoneal chemotherapy (HIPEC) in prevention and therapy of peritoneal m etas- tasis: A systematic review. Pleura and Peritoneum �(2), 51–61 (2022) https://doi.org/10.1515/pp-2021-0152

work page doi:10.1515/pp-2021-0152 2022
[3]

Drugs �� (2), 159–180 (2023) https://doi.org/10.1007/S40265-022-01828-7

Guchelaar, N.A.D., Noordman, B.J., Koolen, S.L.W., Mostert, B., Mads en, E.V.E., Burger, J.W.A., Brandt-Kerkhof, A.R.M., Creemers, G.J., Hingh, I.H.J.T., Luyer, M., Bins, S., Meerten, E., Lagarde, S.M., Verhoef, C., Wijnhoven, B.P.L., Mathijssen, R.H.J.: Intraperitoneal Chemothera py for Unresectable Peritoneal Surface Malignancies. Drugs �� (2), 159–180 ...

work page doi:10.1007/s40265-022-01828-7 2023
[4]

BJS Open �(6), 812–821 (2019) https://doi.org/10.1002/BJS5.50193

Hentzen, J.E.K.R., Plas, W.Y., Constansia, R.D.N., Been, L.B., Hoogwa- ter, F.J.H., Ginkel, R.J., Dam, G.M., Hemmer, P.H.J., Kruijﬀ, S.: Role of diagnostic laparoscopy in patients with suspicion of colorectal pe ri- toneal metastases to evaluate suitability for cytoreductive surg ery with hyperthermic intraperitoneal chemotherapy. BJS Open �(6), 812–821 (...

work page doi:10.1002/bjs5.50193 2019
[5]

(ed.) Clinica l research methodologies in diagnosis and staging of patients with per i- toneal carcinomatosis, pp

Jacquet, P., Sugarbaker, P.H.: In: Sugarbaker, P.H. (ed.) Clinica l research methodologies in diagnosis and staging of patients with per i- toneal carcinomatosis, pp. 359–374. Springer, Boston, MA (199 6). https://doi.org/10.1007/978-1-4613-1247-5 23 . ��

work page doi:10.1007/978-1-4613-1247-5
[6]

European Radiology �� (6), 3101–3112 (2020) https://doi.org/10.1007/s00330-019-06524-x

Sant, I., Engbersen, M.P., Bhairosing, P.A., Lambregts, D.M.J., Bee ts- Tan, R.G.H., Driel, W.J., Aalbers, A.G.J., Kok, N.F.M., Lahaye, M.J.: 11 Diagnostic performance of imaging for the detection of peritoneal metas- tases: a meta-analysis. European Radiology �� (6), 3101–3112 (2020) https://doi.org/10.1007/s00330-019-06524-x

work page doi:10.1007/s00330-019-06524-x 2020
[7]

Journal of Visceral Surgery �� , 293–303 (2018) https://doi.org/10.1016/j.jviscsurg.2018.01.002

Dohan, A., Hobeika, C., Najah, H., Pocard, M., Rousset, P., Eveno , C.: Preoperative assessment of peritoneal carcinomatosis of col- orectal origin. Journal of Visceral Surgery �� , 293–303 (2018) https://doi.org/10.1016/j.jviscsurg.2018.01.002

work page doi:10.1016/j.jviscsurg.2018.01.002 2018
[8]

Jo urnal of surgical oncology �� (6), 565–570 (2010) https://doi.org/10.1002/JSO.21601

Esquivel, J., Chua, T.C., Stojadinovic, A., Melero, J.T., Levine, E.A., G utman, M., Howard, R., Piso, P., Nissan, A., Gomez-Portilla, A., Gonzalez-Bayo n, L., Gonzalez-Moreno, S., Shen, P., Stewart, J.H., Sugarbaker, P.H., Ba rone, R.M., Hoefer, R., Morris, D.L., Sardi, A., Sticca, R.P.: Accuracy and clinical r elevance of computed tomography scan interp...

work page doi:10.1002/jso.21601 2010
[9]

E uropean Radiology 2025, 1–11 (2025) https://doi.org/10.1007/S00330-025-11762-3

Tops-Welten, M.W., Ewals, L.J.S., Hellemond, I.E.G., Piek, J.M.J., Lahaye , M.J., De Hingh, I.H.J.T., Nederend, J., Luyer, M.D.P.: Deﬁning region boundar ies to assess the peritoneal cancer index on imaging: a Delphi study. E uropean Radiology 2025, 1–11 (2025) https://doi.org/10.1007/S00330-025-11762-3

work page doi:10.1007/s00330-025-11762-3 2025
[10]

Informatik aktuell, 22 (2018) https://doi.org/10.1007/978-3-658-25326-4 7

Isensee, F., Petersen, J., Klein, A., Zimmerer, D., Jaeger, P.F., K ohl, S., Wasserthal, J., Koehler, G., Norajitra, T., Wirkert, S., Maier-Hein, K .H.: nnU- Net: Self-adapting Framework for U-Net-Based Medical Image Se gmentation. Informatik aktuell, 22 (2018) https://doi.org/10.1007/978-3-658-25326-4 7

work page doi:10.1007/978-3-658-25326-4 2018
[11]

U-Net: Convolutional Networks for Biomedical Image Segmentation

Ronneberger, O., Fischer, P., Brox, T.: U-Net: Convolutional N etworks for Biomedical Image Segmentation (2015). https://arxiv.org/abs/1505.04597

work page internal anchor Pith review Pith/arXiv arXiv 2015
[12]

Fog simulation on real LiDAR point clouds for 3D object detection in adverse weather,

Liu, Z., Lin, Y., Cao, Y., Hu, H., Wei, Y., Zhang, Z., Lin, S., Guo, B.: Swin Transformer: Hierarchical Vision Transformer using Shifted Windo ws. Proceed- ings of the IEEE International Conference on Computer Vision, 99 92–10002 (2021) https://doi.org/10.1109/ICCV48922.2021.00986

work page doi:10.1109/iccv48922.2021.00986 2021
[13]

Hatamizadeh, A., Nath, V., Tang, Y., Yang, D., Roth, H.R., Xu, D.: S win UNETR: Swin Transformers for Semantic Segmentation of Brain Tum ors in MRI Images. Lecture Notes in Computer Science (including subseries Le cture Notes in Artiﬁcial Intelligence and Lecture Notes in Bioinformatics) �� , 272–284 (2022) https://doi.org/10.1007/978-3-031-08999-2 22

work page doi:10.1007/978-3-031-08999-2 2022
[14]

Hafeez, M., Sattar, A., Farooqui, W.A.: Inter observer reliability for peritoneal carcinomatosis at computed tomography. JPMA. T he Journal of the Pakistan Medical Association �� (5), 973–977 (2023) https://doi.org/10.47391/JPMA.6167 12

work page doi:10.47391/jpma.6167 2023

[1] [1]

European Journal of Cance r �� , 1–2 (2023) https://doi.org/10.1016/J.EJCA.2022.12.008

Rijken, A., Erning, F.N., Rovers, K.P., Lemmens, V.E.P.P., Hingh, I.H.J.T .: On the origin of peritoneal metastases. European Journal of Cance r �� , 1–2 (2023) https://doi.org/10.1016/J.EJCA.2022.12.008

work page doi:10.1016/j.ejca.2022.12.008 2023

[2] [2]

Pleura and Peritoneum �(2), 51–61 (2022) https://doi.org/10.1515/pp-2021-0152

Noiret, B., Piessen, G., Eveno, C.: Update of randomized controlle d tri- als evaluating cytoreductive surgery (CRS) and hyperthermic intr aperitoneal chemotherapy (HIPEC) in prevention and therapy of peritoneal m etas- tasis: A systematic review. Pleura and Peritoneum �(2), 51–61 (2022) https://doi.org/10.1515/pp-2021-0152

work page doi:10.1515/pp-2021-0152 2022

[3] [3]

Drugs �� (2), 159–180 (2023) https://doi.org/10.1007/S40265-022-01828-7

Guchelaar, N.A.D., Noordman, B.J., Koolen, S.L.W., Mostert, B., Mads en, E.V.E., Burger, J.W.A., Brandt-Kerkhof, A.R.M., Creemers, G.J., Hingh, I.H.J.T., Luyer, M., Bins, S., Meerten, E., Lagarde, S.M., Verhoef, C., Wijnhoven, B.P.L., Mathijssen, R.H.J.: Intraperitoneal Chemothera py for Unresectable Peritoneal Surface Malignancies. Drugs �� (2), 159–180 ...

work page doi:10.1007/s40265-022-01828-7 2023

[4] [4]

BJS Open �(6), 812–821 (2019) https://doi.org/10.1002/BJS5.50193

Hentzen, J.E.K.R., Plas, W.Y., Constansia, R.D.N., Been, L.B., Hoogwa- ter, F.J.H., Ginkel, R.J., Dam, G.M., Hemmer, P.H.J., Kruijﬀ, S.: Role of diagnostic laparoscopy in patients with suspicion of colorectal pe ri- toneal metastases to evaluate suitability for cytoreductive surg ery with hyperthermic intraperitoneal chemotherapy. BJS Open �(6), 812–821 (...

work page doi:10.1002/bjs5.50193 2019

[5] [5]

(ed.) Clinica l research methodologies in diagnosis and staging of patients with per i- toneal carcinomatosis, pp

Jacquet, P., Sugarbaker, P.H.: In: Sugarbaker, P.H. (ed.) Clinica l research methodologies in diagnosis and staging of patients with per i- toneal carcinomatosis, pp. 359–374. Springer, Boston, MA (199 6). https://doi.org/10.1007/978-1-4613-1247-5 23 . ��

work page doi:10.1007/978-1-4613-1247-5

[6] [6]

European Radiology �� (6), 3101–3112 (2020) https://doi.org/10.1007/s00330-019-06524-x

Sant, I., Engbersen, M.P., Bhairosing, P.A., Lambregts, D.M.J., Bee ts- Tan, R.G.H., Driel, W.J., Aalbers, A.G.J., Kok, N.F.M., Lahaye, M.J.: 11 Diagnostic performance of imaging for the detection of peritoneal metas- tases: a meta-analysis. European Radiology �� (6), 3101–3112 (2020) https://doi.org/10.1007/s00330-019-06524-x

work page doi:10.1007/s00330-019-06524-x 2020

[7] [7]

Journal of Visceral Surgery �� , 293–303 (2018) https://doi.org/10.1016/j.jviscsurg.2018.01.002

Dohan, A., Hobeika, C., Najah, H., Pocard, M., Rousset, P., Eveno , C.: Preoperative assessment of peritoneal carcinomatosis of col- orectal origin. Journal of Visceral Surgery �� , 293–303 (2018) https://doi.org/10.1016/j.jviscsurg.2018.01.002

work page doi:10.1016/j.jviscsurg.2018.01.002 2018

[8] [8]

Jo urnal of surgical oncology �� (6), 565–570 (2010) https://doi.org/10.1002/JSO.21601

Esquivel, J., Chua, T.C., Stojadinovic, A., Melero, J.T., Levine, E.A., G utman, M., Howard, R., Piso, P., Nissan, A., Gomez-Portilla, A., Gonzalez-Bayo n, L., Gonzalez-Moreno, S., Shen, P., Stewart, J.H., Sugarbaker, P.H., Ba rone, R.M., Hoefer, R., Morris, D.L., Sardi, A., Sticca, R.P.: Accuracy and clinical r elevance of computed tomography scan interp...

work page doi:10.1002/jso.21601 2010

[9] [9]

E uropean Radiology 2025, 1–11 (2025) https://doi.org/10.1007/S00330-025-11762-3

Tops-Welten, M.W., Ewals, L.J.S., Hellemond, I.E.G., Piek, J.M.J., Lahaye , M.J., De Hingh, I.H.J.T., Nederend, J., Luyer, M.D.P.: Deﬁning region boundar ies to assess the peritoneal cancer index on imaging: a Delphi study. E uropean Radiology 2025, 1–11 (2025) https://doi.org/10.1007/S00330-025-11762-3

work page doi:10.1007/s00330-025-11762-3 2025

[10] [10]

Informatik aktuell, 22 (2018) https://doi.org/10.1007/978-3-658-25326-4 7

Isensee, F., Petersen, J., Klein, A., Zimmerer, D., Jaeger, P.F., K ohl, S., Wasserthal, J., Koehler, G., Norajitra, T., Wirkert, S., Maier-Hein, K .H.: nnU- Net: Self-adapting Framework for U-Net-Based Medical Image Se gmentation. Informatik aktuell, 22 (2018) https://doi.org/10.1007/978-3-658-25326-4 7

work page doi:10.1007/978-3-658-25326-4 2018

[11] [11]

U-Net: Convolutional Networks for Biomedical Image Segmentation

Ronneberger, O., Fischer, P., Brox, T.: U-Net: Convolutional N etworks for Biomedical Image Segmentation (2015). https://arxiv.org/abs/1505.04597

work page internal anchor Pith review Pith/arXiv arXiv 2015

[12] [12]

Fog simulation on real LiDAR point clouds for 3D object detection in adverse weather,

Liu, Z., Lin, Y., Cao, Y., Hu, H., Wei, Y., Zhang, Z., Lin, S., Guo, B.: Swin Transformer: Hierarchical Vision Transformer using Shifted Windo ws. Proceed- ings of the IEEE International Conference on Computer Vision, 99 92–10002 (2021) https://doi.org/10.1109/ICCV48922.2021.00986

work page doi:10.1109/iccv48922.2021.00986 2021

[13] [13]

Hatamizadeh, A., Nath, V., Tang, Y., Yang, D., Roth, H.R., Xu, D.: S win UNETR: Swin Transformers for Semantic Segmentation of Brain Tum ors in MRI Images. Lecture Notes in Computer Science (including subseries Le cture Notes in Artiﬁcial Intelligence and Lecture Notes in Bioinformatics) �� , 272–284 (2022) https://doi.org/10.1007/978-3-031-08999-2 22

work page doi:10.1007/978-3-031-08999-2 2022

[14] [14]

Hafeez, M., Sattar, A., Farooqui, W.A.: Inter observer reliability for peritoneal carcinomatosis at computed tomography. JPMA. T he Journal of the Pakistan Medical Association �� (5), 973–977 (2023) https://doi.org/10.47391/JPMA.6167 12

work page doi:10.47391/jpma.6167 2023