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

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  2. Tiago Silveira Gontijo & Marcelo Azevedo Costa, 2020. "Forecasting Hierarchical Time Series in Power Generation," Energies, MDPI, vol. 13(14), pages 1-17, July.
  3. Marlon Mesquita Lopes Cabreira & Felipe Leite Coelho da Silva & Josiane da Silva Cordeiro & Ronald Miguel Serrano Hernández & Paulo Canas Rodrigues & Javier Linkolk López-Gonzales, 2024. "A Hybrid Approach for Hierarchical Forecasting of Industrial Electricity Consumption in Brazil," Energies, MDPI, vol. 17(13), pages 1-15, June.
  4. Katherine Tierney, 2022. "The Future of Assisted Reproductive Technology Live Births in the United States," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 41(5), pages 2289-2309, October.
  5. Wang, Xiaoqian & Hyndman, Rob J. & Wickramasuriya, Shanika L., 2025. "Optimal forecast reconciliation with time series selection," European Journal of Operational Research, Elsevier, vol. 323(2), pages 455-470.
  6. Rombouts, Jeroen & Ternes, Marie & Wilms, Ines, 2025. "Cross-temporal forecast reconciliation at digital platforms with machine learning," International Journal of Forecasting, Elsevier, vol. 41(1), pages 321-344.
  7. Abolghasemi, Mahdi & Tarr, Garth & Bergmeir, Christoph, 2024. "Machine learning applications in hierarchical time series forecasting: Investigating the impact of promotions," International Journal of Forecasting, Elsevier, vol. 40(2), pages 597-615.
  8. Tomokaze Shiratori & Ken Kobayashi & Yuichi Takano, 2020. "Prediction of hierarchical time series using structured regularization and its application to artificial neural networks," PLOS ONE, Public Library of Science, vol. 15(11), pages 1-23, November.
  9. Cengiz, Doruk & Tekgüç, Hasan, 2024. "Counterfactual reconciliation: Incorporating aggregation constraints for more accurate causal effect estimates," International Journal of Forecasting, Elsevier, vol. 40(2), pages 564-580.
  10. Makridakis, Spyros & Spiliotis, Evangelos & Assimakopoulos, Vassilios, 2022. "Predicting/hypothesizing the findings of the M5 competition," International Journal of Forecasting, Elsevier, vol. 38(4), pages 1337-1345.
  11. Yang, Yang & Shang, Han Lin & Raymer, James, 2024. "Forecasting Australian fertility by age, region, and birthplace," International Journal of Forecasting, Elsevier, vol. 40(2), pages 532-548.
  12. Sakai Ando & Futoshi Narita, 2024. "An Alternative Proof of Minimum Trace Reconciliation," Forecasting, MDPI, vol. 6(2), pages 1-6, June.
  13. Lila, Maurício Franca & Meira, Erick & Cyrino Oliveira, Fernando Luiz, 2022. "Forecasting unemployment in Brazil: A robust reconciliation approach using hierarchical data," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
  14. Fernando, Angeline Gautami & Aw, Eugene Cheng-Xi, 2023. "What do consumers want? A methodological framework to identify determinant product attributes from consumers’ online questions," Journal of Retailing and Consumer Services, Elsevier, vol. 73(C).
  15. Zhang, Bohan & Kang, Yanfei & Panagiotelis, Anastasios & Li, Feng, 2023. "Optimal reconciliation with immutable forecasts," European Journal of Operational Research, Elsevier, vol. 308(2), pages 650-660.
  16. Mahsa Ashouri & Rob J Hyndman & Galit Shmueli, 2019. "Fast Forecast Reconciliation Using Linear Models," Monash Econometrics and Business Statistics Working Papers 29/19, Monash University, Department of Econometrics and Business Statistics.
  17. Sbrana, Giacomo & Pelagatti, Matteo, 2024. "Optimal hierarchical EWMA forecasting," International Journal of Forecasting, Elsevier, vol. 40(2), pages 616-625.
  18. Ghelasi, Paul & Ziel, Florian, 2024. "Hierarchical forecasting for aggregated curves with an application to day-ahead electricity price auctions," International Journal of Forecasting, Elsevier, vol. 40(2), pages 581-596.
  19. Yang, Dazhi & van der Meer, Dennis, 2021. "Post-processing in solar forecasting: Ten overarching thinking tools," Renewable and Sustainable Energy Reviews, Elsevier, vol. 140(C).
  20. Eckert, Florian & Hyndman, Rob J. & Panagiotelis, Anastasios, 2021. "Forecasting Swiss exports using Bayesian forecast reconciliation," European Journal of Operational Research, Elsevier, vol. 291(2), pages 693-710.
  21. Héctor M. Zárate-Solano & Norberto Rodríguez-Niño, 2024. "Consumer Prices Trends in Colombia: Detecting Breaks and Forecasting Infation," Borradores de Economia 1289, Banco de la Republica de Colombia.
  22. Athanasopoulos, George & Kourentzes, Nikolaos, 2023. "On the evaluation of hierarchical forecasts," International Journal of Forecasting, Elsevier, vol. 39(4), pages 1502-1511.
  23. Girolimetto, Daniele & Athanasopoulos, George & Di Fonzo, Tommaso & Hyndman, Rob J., 2024. "Cross-temporal probabilistic forecast reconciliation: Methodological and practical issues," International Journal of Forecasting, Elsevier, vol. 40(3), pages 1134-1151.
  24. Colin O. Quinn & George F. Corliss & Richard J. Povinelli, 2024. "Cross-Temporal Hierarchical Forecast Reconciliation of Natural Gas Demand," Energies, MDPI, vol. 17(13), pages 1-18, June.
  25. Sarah Friedrich & Gerd Antes & Sigrid Behr & Harald Binder & Werner Brannath & Florian Dumpert & Katja Ickstadt & Hans A. Kestler & Johannes Lederer & Heinz Leitgöb & Markus Pauly & Ansgar Steland & A, 2022. "Is there a role for statistics in artificial intelligence?," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(4), pages 823-846, December.
  26. Zhang, Bohan & Panagiotelis, Anastasios & Li, Han, 2025. "Constructing hierarchical time series through clustering: Is there an optimal way for forecasting?," International Journal of Forecasting, Elsevier, vol. 41(3), pages 1022-1036.
  27. Robinson Kruse‐Becher, 2025. "Adaptive Now‐ and Forecasting of Global Temperatures Under Smooth Structural Changes," Environmetrics, John Wiley & Sons, Ltd., vol. 36(6), September.
  28. Panagiotelis, Anastasios & Athanasopoulos, George & Gamakumara, Puwasala & Hyndman, Rob J., 2021. "Forecast reconciliation: A geometric view with new insights on bias correction," International Journal of Forecasting, Elsevier, vol. 37(1), pages 343-359.
  29. Han Lin Shang & Yang Yang, 2021. "Forecasting Australian subnational age-specific mortality rates," Journal of Population Research, Springer, vol. 38(1), pages 1-24, March.
  30. Mustapha Sali & Yahya Ghrab & Clément Chatras, 2023. "Optimal product aggregation for sales and operations planning in mass customisation context," Post-Print hal-04319422, HAL.
  31. Anderer, Matthias & Li, Feng, 2022. "Hierarchical forecasting with a top-down alignment of independent-level forecasts," International Journal of Forecasting, Elsevier, vol. 38(4), pages 1405-1414.
  32. Chen, Zhi & Gaba, Anil & Tsetlin, Ilia & Winkler, Robert L., 2022. "Evaluating quantile forecasts in the M5 uncertainty competition," International Journal of Forecasting, Elsevier, vol. 38(4), pages 1531-1545.
  33. Kourentzes, Nikolaos & Saayman, Andrea & Jean-Pierre, Philippe & Provenzano, Davide & Sahli, Mondher & Seetaram, Neelu & Volo, Serena, 2021. "Visitor arrivals forecasts amid COVID-19: A perspective from the Africa team," Annals of Tourism Research, Elsevier, vol. 88(C).
  34. Olivares, Kin G. & Meetei, O. Nganba & Ma, Ruijun & Reddy, Rohan & Cao, Mengfei & Dicker, Lee, 2024. "Probabilistic hierarchical forecasting with deep Poisson mixtures," International Journal of Forecasting, Elsevier, vol. 40(2), pages 470-489.
  35. Wilson, Tom & Grossman, Irina & Temple, Jeromey, 2023. "Evaluation of the best M4 competition methods for small area population forecasting," International Journal of Forecasting, Elsevier, vol. 39(1), pages 110-122.
  36. Bergsteinsson, Hjörleifur G. & Møller, Jan Kloppenborg & Nystrup, Peter & Pálsson, Ólafur Pétur & Guericke, Daniela & Madsen, Henrik, 2021. "Heat load forecasting using adaptive temporal hierarchies," Applied Energy, Elsevier, vol. 292(C).
  37. Brégère, Margaux & Huard, Malo, 2022. "Online hierarchical forecasting for power consumption data," International Journal of Forecasting, Elsevier, vol. 38(1), pages 339-351.
  38. Panagiotelis, Anastasios & Gamakumara, Puwasala & Athanasopoulos, George & Hyndman, Rob J., 2023. "Probabilistic forecast reconciliation: Properties, evaluation and score optimisation," European Journal of Operational Research, Elsevier, vol. 306(2), pages 693-706.
  39. Cengiz, Doruk & Tekgüç, Hasan, 2022. "Counterfactual Reconciliation: Incorporating Aggregation Constraints For More Accurate Causal Effect Estimates," MPRA Paper 114478, University Library of Munich, Germany.
  40. Athanasopoulos, George & Hyndman, Rob J. & Kourentzes, Nikolaos & Panagiotelis, Anastasios, 2024. "Forecast reconciliation: A review," International Journal of Forecasting, Elsevier, vol. 40(2), pages 430-456.
  41. Jeroen Rombouts & Marie Ternes & Ines Wilms, 2024. "Cross-Temporal Forecast Reconciliation at Digital Platforms with Machine Learning," Papers 2402.09033, arXiv.org, revised May 2024.
  42. Zambon, Lorenzo & Agosto, Arianna & Giudici, Paolo & Corani, Giorgio, 2024. "Properties of the reconciled distributions for Gaussian and count forecasts," International Journal of Forecasting, Elsevier, vol. 40(4), pages 1438-1448.
  43. Pritularga, Kandrika F. & Svetunkov, Ivan & Kourentzes, Nikolaos, 2021. "Stochastic coherency in forecast reconciliation," International Journal of Production Economics, Elsevier, vol. 240(C).
  44. Ana Caroline Pinheiro & Paulo Canas Rodrigues, 2024. "Hierarchical Time Series Forecasting of Fire Spots in Brazil: A Comprehensive Approach," Stats, MDPI, vol. 7(3), pages 1-24, June.
  45. Zhang, Bohan & Panagiotelis, Anastasios & Kang, Yanfei, 2024. "Discrete forecast reconciliation," European Journal of Operational Research, Elsevier, vol. 318(1), pages 143-153.
  46. George Athanasopoulos & Nikolaos Kourentzes, 2021. "On the Evaluation of Hierarchical Forecasts," Monash Econometrics and Business Statistics Working Papers 10/21, Monash University, Department of Econometrics and Business Statistics.
  47. Pietro Giorgio Lovaglio, 2025. "Cross‐Learning With Panel Data Modeling for Stacking and Forecast Time Series Employment in Europe," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 44(2), pages 753-780, March.
  48. Sprangers, Olivier & Wadman, Wander & Schelter, Sebastian & de Rijke, Maarten, 2024. "Hierarchical forecasting at scale," International Journal of Forecasting, Elsevier, vol. 40(4), pages 1689-1700.
  49. Bergsteinsson, Hjörleifur G. & Sørensen, Mikkel Lindstrøm & Møller, Jan Kloppenborg & Madsen, Henrik, 2023. "Heat load forecasting using adaptive spatial hierarchies," Applied Energy, Elsevier, vol. 350(C).
  50. Daniele Girolimetto & Tommaso Di Fonzo, 2024. "Point and probabilistic forecast reconciliation for general linearly constrained multiple time series," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 33(2), pages 581-607, April.
  51. Bojer, Casper Solheim, 2022. "Understanding machine learning-based forecasting methods: A decomposition framework and research opportunities," International Journal of Forecasting, Elsevier, vol. 38(4), pages 1555-1561.
  52. Li, Han & Chen, Hua, 2024. "Hierarchical mortality forecasting with EVT tails: An application to solvency capital requirement," International Journal of Forecasting, Elsevier, vol. 40(2), pages 549-563.
  53. Karamaziotis, Panagiotis I. & Raptis, Achilleas & Nikolopoulos, Konstantinos & Litsiou, Konstantia & Assimakopoulos, Vassilis, 2020. "An empirical investigation of water consumption forecasting methods," International Journal of Forecasting, Elsevier, vol. 36(2), pages 588-606.
  54. Vladislav Bína, Jitka Bartosová, Vladimir Pribyl, 2022. "Anomaly Detection in Time Series for Smart Agriculture," International Journal of Management, Knowledge and Learning, ToKnowPress, vol. 11, pages 177-186.
  55. Leprince, Julien & Madsen, Henrik & Møller, Jan Kloppenborg & Zeiler, Wim, 2023. "Hierarchical learning, forecasting coherent spatio-temporal individual and aggregated building loads," Applied Energy, Elsevier, vol. 348(C).
  56. Li, Han & Hyndman, Rob J., 2021. "Assessing mortality inequality in the U.S.: What can be said about the future?," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 152-162.
  57. Gary Koop & Stuart McIntyre & James Mitchell & Aubrey Poon, 2020. "Regional output growth in the United Kingdom: More timely and higher frequency estimates from 1970," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(2), pages 176-197, March.
  58. Hollyman, Ross & Petropoulos, Fotios & Tipping, Michael E., 2021. "Understanding forecast reconciliation," European Journal of Operational Research, Elsevier, vol. 294(1), pages 149-160.
  59. Raffaele Mattera & George Athanasopoulos & Rob Hyndman, 2024. "Improving out-of-sample forecasts of stock price indexes with forecast reconciliation and clustering," Quantitative Finance, Taylor & Francis Journals, vol. 24(11), pages 1641-1667, November.
  60. Sagaert, Yves R. & Kourentzes, Nikolaos, 2025. "Inventory management with leading indicator augmented hierarchical forecasts," Omega, Elsevier, vol. 136(C).
  61. Hakeem‐Ur Rehman & Guohua Wan & Raza Rafique, 2023. "A hybrid approach with step‐size aggregation to forecasting hierarchical time series," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(1), pages 176-192, January.
  62. Nystrup, Peter & Lindström, Erik & Møller, Jan K. & Madsen, Henrik, 2021. "Dimensionality reduction in forecasting with temporal hierarchies," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1127-1146.
  63. Sonaxy Mohanty & Airi Shimamura & Charles D. Nicholson & Andrés D. González & Talayeh Razzaghi, 2025. "Hierarchical Time Series Forecasting of COVID-19 Cases Using County-Level Clustering Data," SN Operations Research Forum, Springer, vol. 6(1), pages 1-28, March.
  64. Emilio Carrizosa & Cristina Molero-Río & Dolores Romero Morales, 2021. "Mathematical optimization in classification and regression trees," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 5-33, April.
  65. Møller, Jan Kloppenborg & Nystrup, Peter & Madsen, Henrik, 2024. "Likelihood-based inference in temporal hierarchies," International Journal of Forecasting, Elsevier, vol. 40(2), pages 515-531.
  66. Wang, Xiaoqian & Hyndman, Rob J. & Li, Feng & Kang, Yanfei, 2023. "Forecast combinations: An over 50-year review," International Journal of Forecasting, Elsevier, vol. 39(4), pages 1518-1547.
  67. Kourentzes, Nikolaos & Athanasopoulos, George, 2021. "Elucidate structure in intermittent demand series," European Journal of Operational Research, Elsevier, vol. 288(1), pages 141-152.
  68. George Athanasopoulos & Nikolaos Kourentzes, 2020. "On the Evaluation of Hierarchical Forecasts," Monash Econometrics and Business Statistics Working Papers 2/20, Monash University, Department of Econometrics and Business Statistics.
  69. Di Fonzo, Tommaso & Girolimetto, Daniele, 2023. "Cross-temporal forecast reconciliation: Optimal combination method and heuristic alternatives," International Journal of Forecasting, Elsevier, vol. 39(1), pages 39-57.
  70. Pritularga, Kandrika F. & Svetunkov, Ivan & Kourentzes, Nikolaos, 2023. "Shrinkage estimator for exponential smoothing models," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1351-1365.
  71. Sakai Ando & Taehoon Kim, 2024. "Systematizing Macroframework Forecasting: High-Dimensional Conditional Forecasting with Accounting Identities," IMF Economic Review, Palgrave Macmillan;International Monetary Fund, vol. 72(4), pages 1386-1410, December.
  72. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
    • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
  73. Di Fonzo, Tommaso & Girolimetto, Daniele, 2024. "Forecast combination-based forecast reconciliation: Insights and extensions," International Journal of Forecasting, Elsevier, vol. 40(2), pages 490-514.
  74. Shafie Bahman & Hamidreza Zareipour, 2025. "Long-Term Multi-Resolution Probabilistic Load Forecasting Using Temporal Hierarchies," Energies, MDPI, vol. 18(11), pages 1-30, June.
  75. George Athanasopoulos & Rob J Hyndman & Mitchell O'Hara-Wild, 2021. "The Road to Recovery from COVID-19 for Australian Tourism," Monash Econometrics and Business Statistics Working Papers 1/21, Monash University, Department of Econometrics and Business Statistics.
  76. Sali, Mustapha & Ghrab, Yahya & Chatras, Clément, 2023. "Optimal product aggregation for sales and operations planning in mass customisation context," International Journal of Production Economics, Elsevier, vol. 263(C).
  77. Abolghasemi, Mahdi & Girolimetto, Daniele & Di Fonzo, Tommaso, 2025. "Improving cross-temporal forecasts reconciliation accuracy and utility in energy market," Applied Energy, Elsevier, vol. 394(C).
  78. Huber, Jakob & Stuckenschmidt, Heiner, 2021. "Intraday shelf replenishment decision support for perishable goods," International Journal of Production Economics, Elsevier, vol. 231(C).
  79. Daniele Girolimetto & George Athanasopoulos & Tommaso Di Fonzo & Rob J Hyndman, 2023. "Cross-temporal Probabilistic Forecast Reconciliation," Monash Econometrics and Business Statistics Working Papers 6/23, Monash University, Department of Econometrics and Business Statistics.
  80. Zeda Li & William W. S. Wei, 2024. "Measuring the advantages of contemporaneous aggregation in forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(5), pages 1308-1320, August.
  81. Florian Eckert & Nina Mühlebach, 2023. "Global and local components of output gaps," Empirical Economics, Springer, vol. 65(5), pages 2301-2331, November.
  82. Aljuneidi, Tariq & Punia, Sushil & Jebali, Aida & Nikolopoulos, Konstantinos, 2024. "Forecasting and planning for a critical infrastructure sector during a pandemic: Empirical evidence from a food supply chain," European Journal of Operational Research, Elsevier, vol. 317(3), pages 936-952.
  83. Kafa, Nadine & Babai, M. Zied & Klibi, Walid, 2025. "Forecasting mail flow: A hierarchical approach for enhanced societal wellbeing," International Journal of Forecasting, Elsevier, vol. 41(1), pages 51-65.
  84. Bartłomiej Gaweł & Andrzej Paliński, 2024. "Global and Local Approaches for Forecasting of Long-Term Natural Gas Consumption in Poland Based on Hierarchical Short Time Series," Energies, MDPI, vol. 17(2), pages 1-25, January.
  85. Corani, Giorgio & Azzimonti, Dario & Rubattu, Nicolò, 2024. "Probabilistic reconciliation of count time series," International Journal of Forecasting, Elsevier, vol. 40(2), pages 457-469.
  86. Meira, Erick & Lila, Maurício Franca & Cyrino Oliveira, Fernando Luiz, 2023. "A novel reconciliation approach for hierarchical electricity consumption forecasting based on resistant regression," Energy, Elsevier, vol. 269(C).
  87. Mikkel L. Sørensen & Peter Nystrup & Mathias B. Bjerregård & Jan K. Møller & Peder Bacher & Henrik Madsen, 2023. "Recent developments in multivariate wind and solar power forecasting," Wiley Interdisciplinary Reviews: Energy and Environment, Wiley Blackwell, vol. 12(2), March.
  88. Paul Ghelasi & Florian Ziel, 2023. "Hierarchical forecasting for aggregated curves with an application to day-ahead electricity price auctions," Papers 2305.16255, arXiv.org.
  89. Spiliotis, Evangelos & Petropoulos, Fotios & Kourentzes, Nikolaos & Assimakopoulos, Vassilios, 2020. "Cross-temporal aggregation: Improving the forecast accuracy of hierarchical electricity consumption," Applied Energy, Elsevier, vol. 261(C).
  90. Rania A. H. Mohamed, 2023. "Enhancing forecast accuracy using combination methods for the hierarchical time series approach," PLOS ONE, Public Library of Science, vol. 18(7), pages 1-18, July.
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