{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T20:00:38Z","timestamp":1769025638034,"version":"3.49.0"},"reference-count":113,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T00:00:00Z","timestamp":1731974400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["MAKE"],"abstract":"<jats:p>Retailers depend on accurate sales forecasts to effectively plan operations and manage supply chains. These forecasts are needed across various levels of aggregation, making hierarchical forecasting methods essential for the retail industry. As competition intensifies, the use of promotions has become a widespread strategy, significantly impacting consumer purchasing behavior. This study seeks to improve forecast accuracy by incorporating promotional data into hierarchical forecasting models. Using a sales dataset from a major Portuguese retailer, base forecasts are generated for different hierarchical levels using ARIMA models and Multi-Layer Perceptron (MLP) neural networks. Reconciliation methods including bottom-up, top-down, and optimal reconciliation with OLS and WLS (struct) estimators are employed. The results show that MLPs outperform ARIMA models for forecast horizons longer than one day. While the addition of regressors enhances ARIMA\u2019s accuracy, it does not yield similar improvements for MLP. MLPs present a compelling balance of simplicity and efficiency, outperforming ARIMA in flexibility while offering faster training times and lower computational demands compared to more complex deep learning models, making them highly suitable for practical retail forecasting applications.<\/jats:p>","DOI":"10.3390\/make6040128","type":"journal-article","created":{"date-parts":[[2024,11,20]],"date-time":"2024-11-20T10:37:35Z","timestamp":1732099055000},"page":"2659-2687","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Enhancing Hierarchical Sales Forecasting with Promotional Data: A Comparative Study Using ARIMA and Deep Neural Networks"],"prefix":"10.3390","volume":"6","author":[{"given":"Mariana","family":"Teixeira","sequence":"first","affiliation":[{"name":"Faculty of Economics, University of Porto, Rua Dr. Roberto Frias, 4200-464 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8516-6418","authenticated-orcid":false,"given":"Jos\u00e9 Manuel","family":"Oliveira","sequence":"additional","affiliation":[{"name":"Faculty of Economics, University of Porto, Rua Dr. Roberto Frias, 4200-464 Porto, Portugal"},{"name":"Institute for Systems and Computer Engineering, Technology and Science, Campus da FEUP, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0959-8446","authenticated-orcid":false,"given":"Patr\u00edcia","family":"Ramos","sequence":"additional","affiliation":[{"name":"Institute for Systems and Computer Engineering, Technology and Science, Campus da FEUP, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"},{"name":"CEOS.PP, ISCAP, Polytechnic of Porto, Rua Jaime Lopes Amorim s\/n, 4465-004 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.dss.2018.08.003","article-title":"Supply chain decision support systems based on a novel hierarchical forecasting approach","volume":"114","author":"Villegas","year":"2018","journal-title":"Decis. Support Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1283","DOI":"10.1016\/j.ijforecast.2019.06.004","article-title":"Retail forecasting: Research and practice","volume":"38","author":"Fildes","year":"2022","journal-title":"Int. J. Forecast."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ejor.2015.11.010","article-title":"Supply chain forecasting: Theory, practice, their gap and the future","volume":"252","author":"Syntetos","year":"2016","journal-title":"Eur. J. Oper. Res."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Oliveira, J.M., and Ramos, P. (2023). Investigating the Accuracy of Autoregressive Recurrent Networks Using Hierarchical Aggregation Structure-Based Data Partitioning. Big Data Cogn. Comput., 7.","DOI":"10.20944\/preprints202304.0222.v1"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1016\/j.ijforecast.2021.11.001","article-title":"Forecasting: Theory and practice","volume":"38","author":"Petropoulos","year":"2022","journal-title":"Int. J. Forecast."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"106380","DOI":"10.1016\/j.cie.2020.106380","article-title":"Demand forecasting in supply chain: The impact of demand volatility in the presence of promotion","volume":"142","author":"Abolghasemi","year":"2020","journal-title":"Comput. Ind. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"107892","DOI":"10.1016\/j.ijpe.2020.107892","article-title":"Demand forecasting in the presence of systematic events: Cases in capturing sales promotions","volume":"230","author":"Abolghasemi","year":"2020","journal-title":"Int. J. Prod. Econ."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/j.rcim.2014.12.015","article-title":"Performance of state space and ARIMA models for consumer retail sales forecasting","volume":"34","author":"Ramos","year":"2015","journal-title":"Robot. Comput.-Integr. Manuf."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.ijforecast.2008.11.010","article-title":"Effective forecasting and judgmental adjustments: An empirical evaluation and strategies for improvement in supply-chain planning","volume":"25","author":"Fildes","year":"2009","journal-title":"Int. J. Forecast."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1016\/j.ijforecast.2012.09.002","article-title":"Measuring forecasting accuracy: The case of judgmental adjustments to SKU-level demand forecasts","volume":"29","author":"Davydenko","year":"2013","journal-title":"Int. J. Forecast."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1002\/for.1129","article-title":"Do experts\u2019 adjustments on model-based SKU-level forecasts improve forecast quality?","volume":"29","author":"Franses","year":"2010","journal-title":"J. Forecast."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"822","DOI":"10.1016\/j.ijforecast.2018.03.001","article-title":"Considerations of a retail forecasting practitioner","volume":"34","author":"Seaman","year":"2018","journal-title":"Int. J. Forecast."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1468","DOI":"10.1016\/j.ijforecast.2021.06.002","article-title":"Applicability of the M5 to Forecasting at Walmart","volume":"38","author":"Seaman","year":"2022","journal-title":"Int. J. Forecast."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1016\/j.ijforecast.2012.10.002","article-title":"Analysis of judgmental adjustments in the presence of promotions","volume":"29","author":"Trapero","year":"2013","journal-title":"Int. J. Forecast."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"626","DOI":"10.1287\/mnsc.46.5.626.12047","article-title":"The Value of Information Sharing in a Two-Level Supply Chain","volume":"46","author":"Lee","year":"2000","journal-title":"Manag. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1108\/02635570110386625","article-title":"Benefits of information sharing with supply chain partnerships","volume":"101","author":"Yu","year":"2001","journal-title":"Ind. Manag. Data Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/j.cie.2007.07.014","article-title":"Is there a benefit to sharing market sales information? Linking theory and practice","volume":"54","author":"Hosoda","year":"2008","journal-title":"Comput. Ind. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"738","DOI":"10.1016\/j.omega.2011.08.009","article-title":"Impact of information exchange on supplier forecasting performance","volume":"40","author":"Trapero","year":"2012","journal-title":"Omega"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"546","DOI":"10.1287\/mnsc.43.4.546","article-title":"Information Distortion in a Supply Chain: The Bullwhip Effect","volume":"43","author":"Lee","year":"1997","journal-title":"Manag. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1504\/IJMTM.2000.001329","article-title":"Information sharing in a supply chain","volume":"1","author":"Lee","year":"2000","journal-title":"Int. J. Manuf. Technol. Manag."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1287\/opre.2014.1326","article-title":"Demand Estimation and Ordering Under Censoring: Stock-Out Timing Is (Almost) All You Need","volume":"63","author":"Jain","year":"2014","journal-title":"Oper. Res."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1287\/opre.1110.1012","article-title":"Estimating Primary Demand for Substitutable Products from Sales Transaction Data","volume":"60","author":"Vulcano","year":"2012","journal-title":"Oper. Res."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1108\/JBIM-04-2018-0126","article-title":"A practical approach to measuring the impacts of stockouts on demand","volume":"34","author":"Kim","year":"2019","journal-title":"J. Bus. Ind. Mark."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/j.ijforecast.2018.11.002","article-title":"Perspectives on supply chain forecasting","volume":"35","author":"Boone","year":"2019","journal-title":"Int. J. Forecast."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1016\/j.ijpe.2011.04.017","article-title":"Safety stock planning under causal demand forecasting","volume":"140","author":"Beutel","year":"2012","journal-title":"Int. J. Prod. Econ."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2401","DOI":"10.1287\/mnsc.2014.1904","article-title":"A Demand Estimation Procedure for Retail Assortment Optimization with Results from Implementations","volume":"60","author":"Fisher","year":"2014","journal-title":"Manag. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1016\/j.bushor.2014.05.003","article-title":"Solving the problems of new product forecasting","volume":"57","author":"Kahn","year":"2014","journal-title":"Bus. Horizons"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1665","DOI":"10.1111\/poms.12846","article-title":"Using Data and Big Data in Retailing","volume":"27","author":"Fisher","year":"2018","journal-title":"Prod. Oper. Manag."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1016\/j.ijforecast.2018.09.003","article-title":"Forecasting sales in the supply chain: Consumer analytics in the big data era","volume":"35","author":"Boone","year":"2019","journal-title":"Int. J. Forecast."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1770","DOI":"10.1111\/poms.12839","article-title":"Can Google Trends Improve Your Sales Forecast?","volume":"27","author":"Boone","year":"2018","journal-title":"Prod. Oper. Manag."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1007\/s10257-014-0265-0","article-title":"A sales forecasting model for consumer products based on the influence of online word-of-mouth","volume":"13","author":"Chern","year":"2015","journal-title":"Inf. Syst. e-Bus. Manag."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1749","DOI":"10.1111\/poms.12707","article-title":"The Operational Value of Social Media Information","volume":"27","author":"Cui","year":"2018","journal-title":"Prod. Oper. Manag."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1775","DOI":"10.1111\/poms.12737","article-title":"Parallel Aspect-Oriented Sentiment Analysis for Sales Forecasting with Big Data","volume":"27","author":"Lau","year":"2018","journal-title":"Prod. Oper. Manag."},{"key":"ref_34","unstructured":"Box, G.E.P., Jenkins, G.M., Reinsel, G.C., and Ljung, G.M. (2015). Time Series Analysis: Forecasting and Control, John Wiley & Sons, Inc.. [5th ed.]."},{"key":"ref_35","first-page":"1","article-title":"Deep learning applications and challenges in big data analytics","volume":"2","author":"Najafabadi","year":"2015","journal-title":"Int. J. Manuf. Technol. Manag."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/S0969-6989(00)00011-4","article-title":"Forecasting aggregate retail sales: A comparison of artificial neural networks and traditional methods","volume":"8","author":"Alon","year":"2001","journal-title":"J. Retail. Consum. Serv."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/S0925-5273(03)00068-9","article-title":"A comparative study of linear and nonlinear models for aggregate retail sales forecasting","volume":"86","author":"Chu","year":"2003","journal-title":"Int. J. Prod. Econ."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1016\/j.ejor.2003.08.037","article-title":"Neural network forecasting for seasonal and trend time series","volume":"160","author":"Zhang","year":"2005","journal-title":"Eur. J. Oper. Res."},{"key":"ref_39","first-page":"359","article-title":"Time series forecasting using neural networks: Should the data be deseasonalized first?","volume":"18","author":"Nelson","year":"1999","journal-title":"J. Predict."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"803","DOI":"10.3846\/16111699.2017.1367324","article-title":"Comparative study on retail sales forecasting between single and combination methods","volume":"18","author":"Aras","year":"2017","journal-title":"J. Bus. Econ. Manag."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.asoc.2005.06.001","article-title":"Improved supply chain management based on hybrid demand forecasts","volume":"7","author":"Aburto","year":"2007","journal-title":"Appl. Soft Comput."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"116993","DOI":"10.1016\/j.eswa.2022.116993","article-title":"Approaching sales forecasting using recurrent neural networks and transformers","volume":"201","author":"Mateo","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","article-title":"Long Short-Term Memory","volume":"9","author":"Hochreiter","year":"1997","journal-title":"Neural Comput."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"106435","DOI":"10.1016\/j.cie.2020.106435","article-title":"An optimized model using LSTM network for demand forecasting","volume":"143","author":"Abbasimehr","year":"2020","journal-title":"Comput. Ind. Eng."},{"key":"ref_45","first-page":"100058","article-title":"Time-series forecasting of seasonal items sales using machine learning\u2014A comparative analysis","volume":"2","author":"Ensafi","year":"2022","journal-title":"Int. J. Inf. Manag. Data Insights"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"993","DOI":"10.1016\/j.procs.2022.01.298","article-title":"Predictive Analytics for Demand Forecasting\u2014A Comparison of SARIMA and LSTM in Retail SCM","volume":"200","author":"Falatouri","year":"2022","journal-title":"Procedia Comput. Sci."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"4964","DOI":"10.1080\/00207543.2020.1735666","article-title":"Deep learning with long short-term memory networks and random forests for demand forecasting in multi-channel retail","volume":"58","author":"Punia","year":"2020","journal-title":"Int. J. Prod. Res."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1108\/IMDS-03-2019-0170","article-title":"Supply chain sales forecasting based on lightGBM and LSTM combination model","volume":"120","author":"Weng","year":"2020","journal-title":"Ind. Manag. Data Syst."},{"key":"ref_49","first-page":"6607","article-title":"Deep Factors for Forecasting","volume":"Volume 97","author":"Chaudhuri","year":"2019","journal-title":"Proceedings of Machine Learning Research, Proceedings of the 36th International Conference on Machine Learning"},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Wang, J., Liu, G.Q., and Liu, L. (2019, January 15\u201318). A Selection of Advanced Technologies for Demand Forecasting in the Retail Industry. Proceedings of the 2019 IEEE 4th International Conference on Big Data Analytics (ICBDA), Suzhou, China.","DOI":"10.1109\/ICBDA.2019.8713196"},{"key":"ref_51","unstructured":"Touretzky, D. (1989). Handwritten Digit Recognition with a Back-Propagation Network. Advances in Neural Information Processing Systems, Morgan-Kaufmann."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.ejor.2020.05.038","article-title":"Retail sales forecasting with meta-learning","volume":"288","author":"Ma","year":"2021","journal-title":"Eur. J. Oper. Res."},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Kaunchi, P., Jadhav, T., Dandawate, Y., and Marathe, P. (2021, January 1\u20133). Future Sales Prediction For Indian Products Using Convolutional Neural Network-Long Short Term Memory. Proceedings of the 2021 2nd Global Conference for Advancement in Technology (GCAT), Bangalore, India.","DOI":"10.1109\/GCAT52182.2021.9587668"},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Liu, Y., Lan, K., Huang, F., Cao, X., Feng, B., and Zhu, B. (2021, January 2\u20134). An Aggregate Store Sales Forecasting Framework based on ConvLSTM. Proceedings of the 2021 5th International Conference on Compute and Data Analysis, ICCDA \u201921, New York, NY, USA.","DOI":"10.1145\/3456529.3456540"},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Nithin, S.S.J., Rajasekar, T., Jayanthy, S., Karthik, K., and Rithick, R.R. (2022, January 16\u201318). Retail Demand Forecasting using CNN-LSTM Model. Proceedings of the 2022 International Conference on Electronics and Renewable Systems (ICEARS), Tuticorin, India.","DOI":"10.1109\/ICEARS53579.2022.9752283"},{"key":"ref_56","first-page":"462","article-title":"Sales Demand Forecast in E-commerce Using a Long Short-Term Memory Neural Network Methodology","volume":"Volume 11955","author":"Bandara","year":"2019","journal-title":"Neural Information Processing, Proceedings of the 26th International Conference, ICONIP 2019, Sydney, Australia, 12\u201315 December 2019"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"112896","DOI":"10.1016\/j.eswa.2019.112896","article-title":"Forecasting across time series databases using recurrent neural networks on groups of similar series: A clustering approach","volume":"140","author":"Bandara","year":"2020","journal-title":"Expert Syst. Appl."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"108148","DOI":"10.1016\/j.patcog.2021.108148","article-title":"Improving the accuracy of global forecasting models using time series data augmentation","volume":"120","author":"Bandara","year":"2021","journal-title":"Pattern Recognit."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/s10660-020-09409-0","article-title":"Study on convolutional neural network and its application in data mining and sales forecasting for E-commerce","volume":"20","author":"Pan","year":"2020","journal-title":"Electron. Commer. Res."},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Chen, K. (2020, January 23\u201325). An Online Retail Prediction Model Based on AGA-LSTM Neural Network. Proceedings of the 2020 2nd International Conference on Machine Learning, Big Data and Business Intelligence (MLBDBI), Taiyuan, China.","DOI":"10.1109\/MLBDBI51377.2020.00032"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"101118","DOI":"10.1016\/j.elerap.2022.101118","article-title":"LSTM with particle Swam optimization for sales forecasting","volume":"51","author":"He","year":"2022","journal-title":"Electron. Commer. Res. Appl."},{"key":"ref_62","first-page":"5998","article-title":"Attention is All you Need","volume":"Volume 30","author":"Vaswani","year":"2017","journal-title":"Advances in Neural Information Processing Systems"},{"key":"ref_63","first-page":"22419","article-title":"Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting","volume":"Volume 34","author":"Wu","year":"2021","journal-title":"Advances in Neural Information Processing Systems"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"1748","DOI":"10.1016\/j.ijforecast.2021.03.012","article-title":"Temporal Fusion Transformers for interpretable multi-horizon time series forecasting","volume":"37","author":"Lim","year":"2021","journal-title":"Int. J. Forecast."},{"key":"ref_65","first-page":"11106","article-title":"Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting","volume":"35","author":"Zhou","year":"2021","journal-title":"Proc. AAAI Conf. Artif. Intell."},{"key":"ref_66","first-page":"27268","article-title":"FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting","volume":"Volume 162","author":"Chaudhuri","year":"2022","journal-title":"Proceedings of Machine Learning Research, Proceedings of the 39th International Conference on Machine Learning"},{"key":"ref_67","unstructured":"Nie, Y., Nguyen, N.H., Sinthong, P., and Kalagnanam, J. (2023, January 1\u20135). A Time Series is Worth 64 Words: Long-term Forecasting with Transformers. Proceedings of the Eleventh International Conference on Learning Representations, Kigali, Rwanda."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"119410","DOI":"10.1016\/j.ins.2023.119410","article-title":"Enhancing time series forecasting: A hierarchical transformer with probabilistic decomposition representation","volume":"647","author":"Tong","year":"2023","journal-title":"Inf. Sci."},{"key":"ref_69","doi-asserted-by":"crossref","unstructured":"Oliveira, J.M., and Ramos, P. (2024). Evaluating the Effectiveness of Time Series Transformers for Demand Forecasting in Retail. Mathematics, 12.","DOI":"10.3390\/math12172728"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1016\/j.ejor.2023.10.039","article-title":"Simplifying tree-based methods for retail sales forecasting with explanatory variables","volume":"314","author":"Wellens","year":"2024","journal-title":"Eur. J. Oper. Res."},{"key":"ref_71","unstructured":"Ansari, A.F., Stella, L., Turkmen, C., Zhang, X., Mercado, P., Shen, H., Shchur, O., Rangapuram, S.S., Arango, S.P., and Kapoor, S. (2024). Chronos: Learning the Language of Time Series. arXiv."},{"key":"ref_72","unstructured":"Woo, G., Liu, C., Kumar, A., Xiong, C., Savarese, S., and Sahoo, D. (2024). Unified Training of Universal Time Series Forecasting Transformers. arXiv."},{"key":"ref_73","unstructured":"Das, A., Kong, W., Sen, R., and Zhou, Y. (2024). A decoder-only foundation model for time-series forecasting. arXiv."},{"key":"ref_74","unstructured":"Rasul, K., Ashok, A., Williams, A.R., Ghonia, H., Bhagwatkar, R., Khorasani, A., Bayazi, M.J.D., Adamopoulos, G., Riachi, R., and Hassen, N. (2024). Lag-Llama: Towards Foundation Models for Probabilistic Time Series Forecasting. arXiv."},{"key":"ref_75","unstructured":"Garza, A., Challu, C., and Mergenthaler-Canseco, M. (2024). TimeGPT-1. arXiv."},{"key":"ref_76","doi-asserted-by":"crossref","unstructured":"Iliadis, L., Maglogiannis, I., Alonso, S., Jayne, C., and Pimenidis, E. (2023). Cross-Learning-Based Sales Forecasting Using Deep Learning via Partial Pooling from Multi-level Data. Engineering Applications of Neural Networks, Springer Nature.","DOI":"10.1007\/978-3-031-34204-2"},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/j.ijforecast.2013.09.006","article-title":"Improving forecasting by estimating time series structural components across multiple frequencies","volume":"30","author":"Kourentzes","year":"2014","journal-title":"Int. J. Forecast."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.ejor.2017.02.046","article-title":"Forecasting with temporal hierarchies","volume":"262","author":"Athanasopoulos","year":"2017","journal-title":"Eur. J. Oper. Res."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1016\/j.ijpe.2004.06.044","article-title":"The impact of aggregation level on forecasting performance","volume":"93\u201394","author":"Zotteri","year":"2005","journal-title":"Int. J. Prod. Econ."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1007\/978-3-030-31150-6_21","article-title":"Hierarchical Forecasting","volume":"Volume 52","author":"Fuleky","year":"2020","journal-title":"Macroeconomic Forecasting in the Era of Big Data"},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/j.ijforecast.2008.07.004","article-title":"Hierarchical forecasts for Australian domestic tourism","volume":"25","author":"Athanasopoulos","year":"2009","journal-title":"Int. J. Forecast."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1002\/for.3980090304","article-title":"Disaggregation methods to expedite product line forecasting","volume":"9","author":"Gross","year":"1990","journal-title":"J. Forecast."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"2579","DOI":"10.1016\/j.csda.2011.03.006","article-title":"Optimal combination forecasts for hierarchical time series","volume":"55","author":"Hyndman","year":"2011","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.csda.2015.11.007","article-title":"Fast computation of reconciled forecasts for hierarchical and grouped time series","volume":"97","author":"Hyndman","year":"2016","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"804","DOI":"10.1080\/01621459.2018.1448825","article-title":"Optimal forecast reconciliation for hierarchical and grouped time series through trace minimization","volume":"114","author":"Wickramasuriya","year":"2019","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"107756","DOI":"10.1016\/j.asoc.2021.107756","article-title":"Hierarchical forecast reconciliation with machine learning","volume":"112","author":"Spiliotis","year":"2021","journal-title":"Appl. Soft Comput."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1016\/j.ejor.2017.04.047","article-title":"Integrated hierarchical forecasting","volume":"263","author":"Pennings","year":"2017","journal-title":"Eur. J. Oper. Res."},{"key":"ref_88","doi-asserted-by":"crossref","unstructured":"Oliveira, J.M., and Ramos, P. (2019). Assessing the Performance of Hierarchical Forecasting Methods on the Retail Sector. Entropy, 21.","DOI":"10.3390\/e21040436"},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1287\/mksc.1050.0135","article-title":"CHAN4CAST: A Multichannel, Multiregion Sales Forecasting Model and Decision Support System for Consumer Packaged Goods","volume":"24","author":"Divakar","year":"2005","journal-title":"Mark. Sci."},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"538","DOI":"10.1016\/j.ijpe.2010.07.007","article-title":"Identifying demand factors for promotional planning and forecasting: A case of a soft drink company in the UK","volume":"128","author":"Ramanathan","year":"2010","journal-title":"Int. J. Prod. Econ."},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"1854","DOI":"10.1111\/poms.12721","article-title":"The Value of Weather Information for E-Commerce Operations","volume":"26","author":"Steinker","year":"2017","journal-title":"Prod. Oper. Manag."},{"key":"ref_92","doi-asserted-by":"crossref","unstructured":"Tan, Y., Takagi, H., and Shi, Y. (2017). Food Sales Prediction with Meteorological Data\u2014A Case Study of a Japanese Chain Supermarket. Data Mining and Big Data, Springer International Publishing.","DOI":"10.1007\/978-3-319-61845-6"},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1108\/IJWBR-07-2020-0035","article-title":"Comparing the day temperature and holiday effects on retail sales of alcoholic beverages\u2014A time-series analysis","volume":"33","author":"Hirche","year":"2021","journal-title":"Int. J. Wine Bus. Res."},{"key":"ref_94","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.jretconser.2019.02.019","article-title":"A data-driven framework for predicting weather impact on high-volume low-margin retail products","volume":"48","author":"Verstraete","year":"2019","journal-title":"J. Retail. Consum. Serv."},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"101921","DOI":"10.1016\/j.jretconser.2019.101921","article-title":"The impact of daily weather on retail sales: An empirical study in brick-and-mortar stores","volume":"52","author":"Badorf","year":"2020","journal-title":"J. Retail. Consum. Serv."},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"5544","DOI":"10.1016\/j.eswa.2010.10.082","article-title":"Identifying the underlying structure of demand during promotions: A structural equation modelling approach","volume":"38","author":"Ramanathan","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"12340","DOI":"10.1016\/j.eswa.2009.04.052","article-title":"SKU demand forecasting in the presence of promotions","volume":"36","author":"Ali","year":"2009","journal-title":"Expert Syst. Appl."},{"key":"ref_98","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/j.ijpe.2015.09.039","article-title":"A hybrid seasonal autoregressive integrated moving average and quantile regression for daily food sales forecasting","volume":"170","author":"Arunraj","year":"2015","journal-title":"Int. J. Prod. Econ."},{"key":"ref_99","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4018\/IJORIS.2016040101","article-title":"Application of SARIMAX Model to Forecast Daily Sales in Food Retail Industry","volume":"7","author":"Arunraj","year":"2016","journal-title":"Int. J. Oper. Res. Inf. Syst."},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"1420","DOI":"10.1016\/j.ijforecast.2020.02.005","article-title":"Daily retail demand forecasting using machine learning with emphasis on calendric special days","volume":"36","author":"Huber","year":"2020","journal-title":"Int. J. Forecast."},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.dss.2013.01.026","article-title":"A multivariate intelligent decision-making model for retail sales forecasting","volume":"55","author":"Guo","year":"2013","journal-title":"Decis. Support Syst."},{"key":"ref_102","doi-asserted-by":"crossref","first-page":"738","DOI":"10.1016\/j.ejor.2014.02.022","article-title":"The value of competitive information in forecasting FMCG retail product sales and the variable selection problem","volume":"237","author":"Huang","year":"2014","journal-title":"Eur. J. Oper. Res."},{"key":"ref_103","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/j.ejor.2015.08.029","article-title":"Demand forecasting with high dimensional data: The case of SKU retail sales forecasting with intra- and inter-category promotional information","volume":"249","author":"Ma","year":"2016","journal-title":"Eur. J. Oper. Res."},{"key":"ref_104","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1057\/jors.2013.174","article-title":"On the identification of sales forecasting models in the presence of promotions","volume":"66","author":"Trapero","year":"2015","journal-title":"J. Oper. Res. Soc."},{"key":"ref_105","unstructured":"Hyndman, R.J., and Athanasopoulos, G. (2021). Forecasting: Principles and Practice, Monash University. [3rd ed.]. Available online: https:\/\/OTexts.com\/fpp3\/."},{"key":"ref_106","first-page":"151","article-title":"A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics","volume":"4","author":"Strimmer","year":"2005","journal-title":"Stat. Appl. Genet. Mol. Biol."},{"key":"ref_107","doi-asserted-by":"crossref","unstructured":"Ramos, P., and Oliveira, J.M. (2016). A procedure for identification of appropriate state space and ARIMA models based on time-series cross-validation. Algorithms, 9.","DOI":"10.3390\/a9040076"},{"key":"ref_108","doi-asserted-by":"crossref","unstructured":"Ramos, P., Oliveira, J.M., Kourentzes, N., and Fildes, R. (2023). Forecasting Seasonal Sales with Many Drivers: Shrinkage or Dimensionality Reduction?. Appl. Syst. Innov., 6.","DOI":"10.3390\/asi6010003"},{"key":"ref_109","doi-asserted-by":"crossref","unstructured":"Ramos, P., and Oliveira, J.M. (2023). Robust Sales forecasting Using Deep Learning with Static and Dynamic Covariates. Appl. Syst. Innov., 6.","DOI":"10.20944\/preprints202308.0427.v1"},{"key":"ref_110","unstructured":"Zhang, A., Lipton, Z.C., Li, M., and Smola, A.J. (2023). Dive into Deep Learning, Cambridge University Press. Available online: https:\/\/D2L.ai."},{"key":"ref_111","unstructured":"Goodfellow, I.J., Bengio, Y., and Courville, A. (2016). Deep Learning, MIT Press. Available online: http:\/\/www.deeplearningbook.org."},{"key":"ref_112","unstructured":"R Development Core Team (2021). R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing."},{"key":"ref_113","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1016\/j.ijforecast.2006.03.001","article-title":"Another look at measures of forecast accuracy","volume":"22","author":"Hyndman","year":"2006","journal-title":"Int. J. Forecast."}],"container-title":["Machine Learning and Knowledge Extraction"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2504-4990\/6\/4\/128\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:35:31Z","timestamp":1760114131000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2504-4990\/6\/4\/128"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,19]]},"references-count":113,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["make6040128"],"URL":"https:\/\/doi.org\/10.3390\/make6040128","relation":{},"ISSN":["2504-4990"],"issn-type":[{"value":"2504-4990","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,11,19]]}}}