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REVIEW 4 major objections 4 minor 32 references

A Comprehensive Forecasting Framework based on Multi-Stage Hierarchical Forecasting Reconciliation and Adjustment

T0 review · 4 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Cut forecast error 3–40% while keeping all levels coherent

desk verdict A genuinely novel industrial reconciliation pipeline with a coherence guarantee that holds, but the one mechanism that makes it new is under-specified and its core premise untested, so the accuracy claim is conditional. read the letter →

arxiv 2412.14718 v1 pith:BPS5PZZ3 submitted 2024-12-19 cs.LG cs.DC

Zhengchao Yang , Mithun Ghosh , Anish Saha , Dong Xu , Konstantin Shmakov , Kuang-chih Lee This is my paper · ORCID
classification cs.LGcs.DC
keywords hierarchicaltimeseriesforecastingforecastreconciliationcoherenceBayesianoptimizationensembleFFTseasonalityharmonicalignmentMinTraceadsdemand
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that hierarchical time-series forecasting does not have to choose between coherence (children summing exactly to parents) and accuracy. It introduces Multi-Stage HiFoReAd, a four-stage pipeline that takes independent forecasts from a Bayesian-optimized ensemble of LGBM, MSTL, and Prophet, then reconciles them level by level: Top-Down disaggregation, harmonic alignment via FFT-based seasonal similarity, MinTrace reconciliation on the top three levels, and stratified scaling on the bottom level. On Walmart's ad-demand data and three public datasets, the framework reports average APE improvements of 3% to 40% over the un-reconciled ensemble and 1.2% to 92.9% over deep-learning baselines, while guaranteeing that all levels are coherent. A sympathetic reader would care because the paper addresses a practical trade-off that matters in production forecasting: reconciliation methods often degrade lower-level accuracy, and the authors claim their seasonal-similarity weighting avoids that degradation.

What carries the argument

The machinery is the Multi-Stage HiFoReAd pipeline, whose load-bearing component is the harmonic alignment step (HHAFA). For each time series, the dominant seasonal components are extracted via FFT and represented as seasonality values $s_i$; after a ceiling quantization, the Jaccard similarity $J(\lceil s_k^i\rceil, \lceil s_1\rceil)$ between a lower-level series and the top-level series determines how much of the Top-Down forecast vs. the original BO-ensemble forecast is used for that series. This same similarity, applied between parent and child in the bottom two levels, drives the Stratified Scale-Weighted Forecasts Synchronization (SSW-FS). MinTrace with WLS then reconciles the top three levels while deliberately excluding the noisy bottom level.

What would settle it

Compute the HHAFA blend weights on a dataset where a child series has a clear seasonal pattern that is absent in its parent (or vice versa) and compare against a version that uses a fixed blend weight; if the Jaccard-guided weights do not improve out-of-sample APE over the fixed-weight version, the load-bearing assumption is not supported. Also, re-running with different values of the unspecified threshold $\tau$ and ceiling constant $c$ would reveal whether the reported improvements are sensitive to these hidden hyperparameters.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that a multi-stage reconciliation pipeline can preserve each time series' intrinsic seasonality while enforcing hierarchy-wide coherence, and that doing so improves rather than sacrifices accuracy. The key move is to use the Jaccard similarity between the ceiling-quantized FFT seasonal components of a child series and its parent as a per-series blending weight between Top-Down forecasts and the original ensemble forecasts. The authors report that this 'harmonic alignment', followed by MinTrace WLS on the top three levels and a scale-weighted synchronization on the bottom two levels, yields coherent forecasts on all four datasets with APE reductions in most level-wise comparisons.

Load-bearing premise

The method assumes that the Jaccard similarity between ceiling-quantized FFT seasonal components of a child and its parent is a reliable and stable measure of how much to trust top-down versus bottom-up forecasts at that node.

Editorial extensions

If this is right

  • Production forecasting systems can enforce exact aggregation constraints across a hierarchy without the usual accuracy penalty at lower levels.
  • The seasonal-similarity weighting suggests that the degree of trust in top-down vs. bottom-up information should vary per series, not be fixed globally.
  • Excluding the bottom level from MinTrace and treating bottom-level reconciliation separately can protect higher levels from sparse, noisy data.
  • The reported speedups on large datasets imply the staged design is compatible with distributed execution in practice.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A testable extension is to replace the ceiling-quantized Jaccard similarity with other seasonal-similarity measures and see whether the blend weight's sensitivity to $\tau$ and $c$ disappears; the paper leaves those hyperparameters unspecified.
  • The negative level-wise APE changes on Walmart level 2 and Tourism level 2 suggest the method's benefit is concentrated in levels where top-down information is informative; a diagnostic that reports per-level Jaccard distributions would tell practitioners when the method is safe.
  • The claim that the framework preserves seasonality is only indirectly tested via APE; a direct comparison of reconciled vs. raw seasonal spectra would isolate whether harmonic alignment actually preserves the intended seasonal components or merely shifts errors.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper proposes Multi-Stage HiFoReAd, a hierarchical forecasting framework with four stages: top-down reconciliation, a seasonality-based adjustment step called HHAFA, MinTrace WLS reconciliation applied to the top three levels, and a stratified scaling step (SSW-FS) for the bottom level. The framework is evaluated on one internal Walmart ads-demand dataset and three public datasets, all with four hierarchical levels, and the paper reports coherent forecasts with APE improvements relative to a Bayesian-optimized ensemble of LGBM, MSTL+ETS, and Prophet, as well as relative to several state-of-the-art deep learning and reconciliation baselines.

Significance. If the accuracy claims hold, the framework would be a practically valuable contribution: it guarantees coherence by construction while preserving per-series seasonality, it is designed for distributed implementation at industrial scale, and it is evaluated on both private and public data. The paper also provides a useful decomposition of the reconciliation problem into stages. However, the central accuracy claim rests on the HHAFA and SSW-FS similarity mechanism, which is under-specified and not empirically validated; as written, the reported improvements are not reproducible from the text alone. The coherence claim, in contrast, is sound by construction.

major comments (4)
  1. [III-C(b)] The definition of the seasonal similarity signal is internally inconsistent and under-specified. The paper first defines s_i as a scalar sum over 'domminant frequencies' of |ϑ_f| cos(arg(ϑ_f)), then writes s_i = {s | s ≤ τ}, i.e., as a set. If s_i is a scalar, the Jaccard similarity J(⌈s_i⌉, ⌈s_1⌉) degenerates to 0 or 1, turning the HHAFA blend into a hard switch between top-down and BO forecasts. If s_i is a set, the threshold τ, the criterion for selecting dominant frequencies, and the ceiling constant c in ⌈⌉*(c) are never specified. The formulas in III-C(b) and III-C(d) are load-bearing for the claimed accuracy gains, so the authors must state the exact quantities and give the parameter values used in the experiments.
  2. [III-C(b), III-C(d), Table II] The paper provides no evidence for the core premise that high Jaccard similarity of FFT-derived seasonal components between a child and its parent predicts that top-down forecasts are more accurate than the BO ensemble. This premise drives HHAFA and SSW-FS, yet no ablation, sensitivity analysis, or correlation test is reported. The negative APE changes in Table II—Walmart level 2 mean APE worsens by 9.69% and Tourism level 2 worsens by 7.51% (mean) and 10.76% (median) compared with the BO ensemble—are consistent with the similarity weight being mis-calibrated. The authors should report per-series comparisons of APE(TD) versus APE(BO) as a function of the Jaccard score, or otherwise validate the mechanism directly.
  3. [III-B and V-A] The reported improvements are not accompanied by significance tests or confidence intervals, and the evaluation protocol creates a risk of selection bias. The model hyperparameters and BO ensemble weights are chosen by minimizing the average APE over the four cross-validation sets (Section III-B), and the reported level-wise APEs are also averaged over those same cross-validation 'test' sets (Section V-A). The paper should clarify whether the reported numbers are from a genuinely separate holdout within each CV fold and should provide standard errors, confidence intervals, or paired significance tests. This matters because several claimed improvements are small (e.g., 1.22% in Table IV, 2.50% in Table II).
  4. [Table II and Abstract] The abstract claims the framework improves average APE by 3% to 40% across levels relative to the BO ensemble, but Table II shows that the final forecasts are worse than the BO ensemble at several levels and medians, including Walmart level 2 mean (−9.69%) and Tourism level 2 mean and median (−7.51% and −10.76%). The claim should be restated per level or as an explicit average over levels, and the authors should discuss the degradation cases rather than only the improvements.
minor comments (4)
  1. [IV-B] The subsection heading 'Road Traffic Data, M3, Tourism' appears to contain a typo: the public dataset used is M5, not M3.
  2. [III-C(b)] The notation is unclear in several places: 'domminant frequencies' should be 'dominant frequencies'; the expression '⌈⌉*(c)' does not define how the ceiling constant c is applied; and the symbol J is used both for the Jaccard similarity and as an index set in Section III-B, which is confusing.
  3. [Figure 5 caption] The caption contains 'sumps these forecasts' and should read 'sums these forecasts'.
  4. [III-C(c)] The estimation of the MinTrace WLS covariance matrix W_h is described only as 'we adopt WLS since it gives the best results.' To make the reconciliation step reproducible, the exact estimator used for W_h should be specified (e.g., diagonal OLS, shrinkage, or a particular residual-based estimator).

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: coherence is constructed, accuracy claims are empirical, and no self-citation chain is load-bearing.

full rationale

The paper's core claims are empirical evaluations of a pipeline, not consequences of definitions. Coherence is enforced by the MinTrace WLS aggregation and by the SSW-FS proportional scaling equation; these make the hierarchical sums equal by construction, but the paper does not present this as a derived predictive result—it explicitly lists it as a design stage. The HHAFA forecast is a convex combination of Top-Down and BO-ensemble forecasts with weights computed from FFT-seasonality Jaccard similarity; the weights are not fitted to the reported APE, so the reported improvements over the BO ensemble and SOTA models are independent empirical outcomes. The under-specified threshold tau and ceiling constant c, and the inconsistent definition of s_i as both a scalar and a set, are reproducibility and under-specification concerns, not circular reductions. There are no load-bearing self-citations and no renamed quantity that is equivalent to its own input by construction.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The framework rests on several unstated or unspecified choices: the seasonality threshold and ceiling constant in HHAFA, the historical window L, the W_h estimator, and per-series BO weights and hyperparameters. The most consequential assumption is that seasonality similarity between parent and child is a reliable signal for blending forecasts.

free parameters (7)
  • HHAFA seasonality threshold tau
    Section III-C(b) removes seasonality values based on tau, but the value is never reported; final forecast accuracy depends on this cutoff.
  • HHAFA ceiling constant c
    The ceiling operation is applied to seasonal components before Jaccard similarity; c is not specified and affects the similarity weights.
  • Top-down historical proportion window L
    Section III-C(a) averages historical proportions over the last L periods; L is not given.
  • BO ensemble weights w1, w2, w3 = not reported
    Per time series weights for LGBM, Prophet, and MSTL are chosen by minimizing APE on validation sets; no weights or ranges are reported.
  • Per-series model hyperparameters phi_iM = not reported
    Hyperparameters for each base model and time series are optimized by minimizing average validation APE, as described in Section III-B; the optimizer and resulting values are unspecified.
  • MinTrace WLS covariance matrix W_h = estimated from data
    Section III-C(c) uses WLS for W_h but does not specify the estimator; the reconciliation matrix depends directly on this choice.
  • FFT dominant frequency selection
    The seasonal component keeps only dominant frequencies from the periodogram; the selection rule and number of frequencies are not stated.
assumptions (6)
  • standard math Aggregation matrix identity y_t = S b_t holds for historical data
    Standard hierarchical time series structure used throughout Section III-C.
  • domain assumption Jaccard similarity of ceiling-quantized seasonal components reflects the predictive usefulness of parent seasonality for children
    Core of HHAFA and SSW-FS; the paper provides only a qualitative claim that it captures similar seasonal patterns.
  • domain assumption Excluding the bottom level from MinTrace and reconciling only the top three levels improves accuracy
    Section III-C(c) asserts that bottom-level noise and sparsity harm reconciliation; this is plausible but not demonstrated separately.
  • domain assumption MinTrace WLS assumptions are acceptable even though base forecasts may be biased or non-Gaussian
    The authors note these assumptions often fail in Section II, yet proceed with WLS and choose it because it gives the best results.
  • standard math FFT-based seasonal components and dominant frequencies adequately capture seasonality of each series
    FFT is standard, but truncation to dominant frequencies is a modeling choice with no stability check.
  • domain assumption Four cross-validation sets are sufficient for comparing methods without overfitting to validation choices
    Hyperparameters and thresholds are selected on validation sets; no separate holdout is reported.

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Pith. "Pith review of A Comprehensive Forecasting Framework based on Multi-Stage Hierarchical Forecasting Reconciliation and Adjustment." pith.science (2026). https://pith.science/paper/BPS5PZZ3

@misc{pith2026241214718,
  author       = {Pith},
  title        = {Pith review of: A Comprehensive Forecasting Framework based on Multi-Stage Hierarchical Forecasting Reconciliation and Adjustment},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BPS5PZZ3}},
  note         = {Machine review of arXiv:2412.14718}
}
read the original abstract

Ads demand forecasting for Walmart's ad products plays a critical role in enabling effective resource planning, allocation, and management of ads performance. In this paper, we introduce a comprehensive demand forecasting system that tackles hierarchical time series forecasting in business settings. Though traditional hierarchical reconciliation methods ensure forecasting coherence, they often trade off accuracy for coherence especially at lower levels and fail to capture the seasonality unique to each time-series in the hierarchy. Thus, we propose a novel framework "Multi-Stage Hierarchical Forecasting Reconciliation and Adjustment (Multi-Stage HiFoReAd)" to address the challenges of preserving seasonality, ensuring coherence, and improving accuracy. Our system first utilizes diverse models, ensembled through Bayesian Optimization (BO), achieving base forecasts. The generated base forecasts are then passed into the Multi-Stage HiFoReAd framework. The initial stage refines the hierarchy using Top-Down forecasts and "harmonic alignment." The second stage aligns the higher levels' forecasts using MinTrace algorithm, following which the last two levels undergo "harmonic alignment" and "stratified scaling", to eventually achieve accurate and coherent forecasts across the whole hierarchy. Our experiments on Walmart's internal Ads-demand dataset and 3 other public datasets, each with 4 hierarchical levels, demonstrate that the average Absolute Percentage Error from the cross-validation sets improve from 3% to 40% across levels against BO-ensemble of models (LGBM, MSTL+ETS, Prophet) as well as from 1.2% to 92.9% against State-Of-The-Art models. In addition, the forecasts at all hierarchical levels are proved to be coherent. The proposed framework has been deployed and leveraged by Walmart's ads, sales and operations teams to track future demands, make informed decisions and plan resources.

Figures

Figures reproduced from arXiv: 2412.14718 by the authors.

Figure 1
Figure 1. The Framework Design of the Proposed Demand Forecasting System [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Back-testing framework for Walmart Connect Ads Demand data, [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 2
Figure 2. The Hierarchical Time Series Structure with 4 Levels [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: The Multi-Stage Hierarchical Forecasting Reconciliation and Adjust [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: The Hierarchical Time Series Structure in a matrix formulation. (a) A [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 6
Figure 6. Figure 6: Stratified Scale-Weighted Forecasts Synchronization [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]
Figure 7
Figure 7. Figure 7: Sampled visualization of cross-validation forecasts between various [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

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Reference graph

Works this paper leans on

32 extracted references · 26 canonical work pages

  1. [1]

    Manufacturer’s cooperative advertising, demand uncertainty, and information sharing,

    R. Yan, Z. Cao, and Z. Pei, “Manufacturer’s cooperative advertising, demand uncertainty, and information sharing,” Journal of Business Research, vol. 69, no. 2, pp. 709–717, 2016

    work page 2016

  2. [2]

    A request-level guaranteed delivery advertising planning: Forecasting and allocation,

    H. Zhang, L. Zhang, L. Xu, X. Ma, Z. Wu, C. Tang, W. Xu, and Y . Yang, “A request-level guaranteed delivery advertising planning: Forecasting and allocation,” in Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining , 2020, pp. 2980– 2988

    work page 2020

  3. [3]

    The bullwhip effect in supply chains,

    H. L. Lee, V . Padmanabhan, and S. Whang, “The bullwhip effect in supply chains,” 1997

    work page 1997

  4. [4]

    Model selection in reconciling hierarchical time series,

    M. Abolghasemi, R. J. Hyndman, E. Spiliotis, and C. Bergmeir, “Model selection in reconciling hierarchical time series,” Machine Learning, pp. 1–51, 2022

    work page 2022

  5. [5]

    Optimally reconciling forecasts in a hierarchy,

    R. J. Hyndman, G. Athanasopoulos et al. , “Optimally reconciling forecasts in a hierarchy,”Foresight: The International Journal of Applied Forecasting, no. 35, pp. 42–48, 2014

    work page 2014

  6. [6]

    Forecasting at scale,

    S. J. Taylor and B. Letham, “Forecasting at scale,” The American Statistician, vol. 72, no. 1, pp. 37–45, 2018

    2018

  7. [7]

    Short-term load forecasting for industrial customers based on tcn-lightgbm,

    Y . Wang, J. Chen, X. Chen, X. Zeng, Y . Kong, S. Sun, Y . Guo, and Y . Liu, “Short-term load forecasting for industrial customers based on tcn-lightgbm,” IEEE Transactions on Power Systems, vol. 36, no. 3, pp. 1984–1997, 2020

    work page 1984

  8. [8]

    Bitcoin fore- casting using arima and prophet,

    I. Yenido ˘gan, A. Çayir, O. Kozan, T. Da ˘g, and Ç. Arslan, “Bitcoin fore- casting using arima and prophet,” in 2018 3rd international conference on computer science and engineering (UBMK) . IEEE, 2018, pp. 621– 624

    work page 2018

Show all 32 references
  1. [9]

    Hierarchical time series forecasting via support vector regression in the european travel retail industry,

    J. P. Karmy and S. Maldonado, “Hierarchical time series forecasting via support vector regression in the european travel retail industry,” Expert Systems with Applications , vol. 137, pp. 59–73, 2019

    2019

  2. [10]

    Integrated hierarchical forecasting,

    C. L. Pennings and J. Van Dalen, “Integrated hierarchical forecasting,” European Journal of Operational Research, vol. 263, no. 2, pp. 412–418, 2017

    2017

  3. [11]

    Supply chain decision support systems based on a novel hierarchical forecasting approach,

    M. A. Villegas and D. J. Pedregal, “Supply chain decision support systems based on a novel hierarchical forecasting approach,” Decision Support Systems, vol. 114, pp. 29–36, 2018

    2018

  4. [12]

    Combining forecasts: A review and annotated bibliog- raphy,

    R. T. Clemen, “Combining forecasts: A review and annotated bibliog- raphy,” International journal of forecasting , vol. 5, no. 4, pp. 559–583, 1989

    1989

  5. [13]

    The accu- racy of extrapolation (time series) methods: Results of a forecasting competition,

    S. Makridakis, A. Andersen, R. Carbone, R. Fildes, M. Hibon, R. Lewandowski, J. Newton, E. Parzen, and R. Winkler, “The accu- racy of extrapolation (time series) methods: Results of a forecasting competition,” Journal of forecasting , vol. 1, no. 2, pp. 111–153, 1982

    1982

  6. [14]

    The m2-competition: A real-time judgmentally based forecasting study,

    S. Makridakis, C. Chatfield, M. Hibon, M. Lawrence, T. Mills, K. Ord, and L. F. Simmons, “The m2-competition: A real-time judgmentally based forecasting study,” International Journal of forecasting , vol. 9, no. 1, pp. 5–22, 1993

    1993

  7. [15]

    Demand forecasting in supply chains: a review of aggregation and hierarchical approaches,

    M. Z. Babai, J. E. Boylan, and B. Rostami-Tabar, “Demand forecasting in supply chains: a review of aggregation and hierarchical approaches,” International Journal of Production Research , vol. 60, no. 1, pp. 324– 348, 2022

    2022

  8. [16]

    A greedy aggregation–decomposition method for intermittent demand forecasting in fashion retailing,

    C. Li and A. Lim, “A greedy aggregation–decomposition method for intermittent demand forecasting in fashion retailing,” European Journal of Operational Research , vol. 269, no. 3, pp. 860–869, 2018

    2018

  9. [17]

    Non- stationary demand forecasting by cross-sectional aggregation,

    B. Rostami-Tabar, M. Z. Babai, Y . Ducq, and A. Syntetos, “Non- stationary demand forecasting by cross-sectional aggregation,” Interna- tional Journal of Production Economics , vol. 170, pp. 297–309, 2015

    2015

  10. [18]

    A model for selecting the appropriate level of aggregation in forecasting processes,

    G. Zotteri and M. Kalchschmidt, “A model for selecting the appropriate level of aggregation in forecasting processes,” International Journal of Production Economics, vol. 108, no. 1-2, pp. 74–83, 2007

    2007

  11. [19]

    Regularized regression for hierarchical forecasting without unbiasedness conditions,

    S. Ben Taieb and B. Koo, “Regularized regression for hierarchical forecasting without unbiasedness conditions,” in Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, 2019, pp. 1337–1347

    2019

  12. [20]

    Optimal forecast reconciliation for hierarchical and grouped time series through trace minimization,

    S. L. Wickramasuriya, G. Athanasopoulos, and R. J. Hyndman, “Optimal forecast reconciliation for hierarchical and grouped time series through trace minimization,” Journal of the American Statistical Association , 2018

    2018

  13. [21]

    A machine learning approach for forecasting hierarchical time series,

    P. Mancuso, V . Piccialli, and A. M. Sudoso, “A machine learning approach for forecasting hierarchical time series,” Expert Systems with Applications, vol. 182, p. 115102, 2021

    2021

  14. [22]

    Hierarchical forecast reconciliation with machine learning,

    E. Spiliotis, M. Abolghasemi, R. J. Hyndman, F. Petropoulos, and V . Assimakopoulos, “Hierarchical forecast reconciliation with machine learning,” Applied Soft Computing , vol. 112, p. 107756, 2021

    2021

  15. [23]

    Lightgbm: A highly efficient gradient boosting decision tree,

    G. Ke, Q. Meng, T. Finley, T. Wang, W. Chen, W. Ma, Q. Ye, and T.- Y . Liu, “Lightgbm: A highly efficient gradient boosting decision tree,” Advances in neural information processing systems , vol. 30, 2017

    2017

  16. [24]

    Mstl: A seasonal-trend decomposition algorithm for time series with multiple seasonal patterns,

    K. Bandara, R. J. Hyndman, and C. Bergmeir, “Mstl: A seasonal-trend decomposition algorithm for time series with multiple seasonal patterns,” arXiv preprint arXiv:2107.13462 , 2021

    2021 arXiv

  17. [25]

    Modified top down approach for hierarchical forecasting in a beverage supply chain,

    D. Mir ˇceti´c, S. Nikoliˇci´c, Ð. Stojanovi´c, and M. Maslari´c, “Modified top down approach for hierarchical forecasting in a beverage supply chain,” Transportation research procedia, vol. 22, pp. 193–202, 2017

    2017

  18. [26]

    Forecast- ing hierarchical time series in supply chains: an empirical investigation,

    D. Mircetic, B. Rostami-Tabar, S. Nikolicic, and M. Maslaric, “Forecast- ing hierarchical time series in supply chains: an empirical investigation,” International Journal of Production Research , vol. 60, no. 8, pp. 2514– 2533, 2022

    2022

  19. [27]

    P. J. B. R. A. Davis, Introduction to time series and forecasting. springer publication, 2016

    2016

  20. [28]

    Identifying seasonality in time series by applying fast fourier transform,

    H. Musbah, M. El-Hawary, and H. Aly, “Identifying seasonality in time series by applying fast fourier transform,” in2019 IEEE Electrical Power and Energy Conference (EPEC) . IEEE, 2019, pp. 1–4

    2019

  21. [29]

    Fast global alignment kernels,

    M. Cuturi, “Fast global alignment kernels,” in Proceedings of the 28th international conference on machine learning (ICML-11) , 2011, pp. 929–936

    2011

  22. [30]

    Pyraformer: Low-complexity pyramidal attention for long-range time series modeling and forecasting,

    S. Liu, H. Yu, C. Liao, J. Li, W. Lin, A. X. Liu, and S. Dustdar, “Pyraformer: Low-complexity pyramidal attention for long-range time series modeling and forecasting,” inInternational conference on learning representations, 2021

    2021

  23. [31]

    Fedformer: Frequency enhanced decomposed transformer for long-term series fore- casting,

    T. Zhou, Z. Ma, Q. Wen, X. Wang, L. Sun, and R. Jin, “Fedformer: Frequency enhanced decomposed transformer for long-term series fore- casting,” in International Conference on Machine Learning . PMLR, 2022, pp. 27 268–27 286

    2022

  24. [32]

    Long-term forecasting with tide: Time-series dense encoder,

    A. Das, W. Kong, A. Leach, R. Sen, and R. Yu, “Long-term forecasting with tide: Time-series dense encoder,” arXiv preprint arXiv:2304.08424, 2023

    2023 arXiv

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