{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T16:30:23Z","timestamp":1783009823501,"version":"3.54.5"},"reference-count":42,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2024,12,1]],"date-time":"2024-12-01T00:00:00Z","timestamp":1733011200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Intelligent Data Analysis: An International Journal"],"published-print":{"date-parts":[[2025,7]]},"abstract":"<jats:p>Accurate sales forecasting of fresh food is imperative for retailers. It facilitates maintaining optimal inventory levels, thereby enhancing customer satisfaction, boosting revenue, and minimizing waste. However, sales sequences of fresh food are subject to multiple compounded factors, exhibiting nonlinearity and non-stationarity, posing challenges for prediction. This paper proposes a novel multi-variable hybrid model, VMD-LSTM-BMA, based on variational mode decomposition (VMD), long short-term memory (LSTM) neural networks, and Bayesian model averaging (BMA), for daily fresh food sales forecasting. Utilizing the posterior distribution generated by BMA, we calculate prediction intervals at various confidence levels to quantify the uncertainty of the forecasting outcomes.\u00a0Employing a daily banana sales dataset from a retail chain supermarket, we validate the predictive performance of the proposed hybrid model at different aggregation levels. The results demonstrate that our VMD-LSTM-BMA framework achieves superior point forecasting accuracy compared to other models. In most instances, the prediction intervals provided by VMD-LSTM-BMA exhibit a higher prediction interval coverage probability (PICP) and a narrower interval width. Our proposed hybrid model operates robustly and efficiently, capable of providing reliable guidance for retailers\u2019 replenishment and ordering processes, thereby mitigating the risks of out-of-stock and excess inventory.<\/jats:p>","DOI":"10.1177\/1088467x241296754","type":"journal-article","created":{"date-parts":[[2025,7,9]],"date-time":"2025-07-09T14:15:53Z","timestamp":1752070553000},"page":"982-998","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["VMD-LSTM-BMA: A hybrid model for enhancing fresh food sales forecasting and uncertainty estimation"],"prefix":"10.1177","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-1840-0371","authenticated-orcid":false,"given":"Shangxue","family":"Luo","sequence":"first","affiliation":[{"name":"Department of Data Science, School of Statistics, Capital University of Economics and Business, Beijing, China"},{"name":"China Consumption Big Data Academy, Capital University of Economics and Business, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhenkun","family":"Zhou","sequence":"additional","affiliation":[{"name":"Department of Data Science, School of Statistics, Capital University of Economics and Business, Beijing, China"},{"name":"China Consumption Big Data Academy, Capital University of Economics and Business, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tao","family":"Ren","sequence":"additional","affiliation":[{"name":"Department of Data Science, School of Statistics, Capital University of Economics and Business, Beijing, China"},{"name":"China Consumption Big Data Academy, Capital University of Economics and Business, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2024,12]]},"reference":[{"key":"e_1_3_4_2_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-169014"},{"key":"e_1_3_4_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2018.04.034"},{"key":"e_1_3_4_4_2","doi-asserted-by":"publisher","DOI":"10.1002\/j.2158-1592.2008.tb00090.x"},{"key":"e_1_3_4_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2017.01.022"},{"key":"e_1_3_4_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2009.04.052"},{"key":"e_1_3_4_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.rcim.2014.12.015"},{"key":"e_1_3_4_8_2","doi-asserted-by":"publisher","DOI":"10.1108\/01443571211230925"},{"key":"e_1_3_4_9_2","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199641178.001.0001"},{"key":"e_1_3_4_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.dss.2013.10.008"},{"key":"e_1_3_4_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2012.07.002"},{"key":"e_1_3_4_12_2","doi-asserted-by":"publisher","DOI":"10.3233\/IDA-205103"},{"key":"e_1_3_4_13_2","doi-asserted-by":"publisher","DOI":"10.2478\/v10051-008-0013-7"},{"key":"e_1_3_4_14_2","doi-asserted-by":"publisher","DOI":"10.4018\/ijisscm.2013070105"},{"key":"e_1_3_4_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10288-016-0316-0"},{"key":"e_1_3_4_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2023.110283"},{"key":"e_1_3_4_17_2","doi-asserted-by":"publisher","DOI":"10.1080\/00207543.2020.1844332"},{"key":"e_1_3_4_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jretai.2021.01.003"},{"key":"e_1_3_4_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2008.09.048"},{"key":"e_1_3_4_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.dss.2010.12.002"},{"key":"e_1_3_4_21_2","doi-asserted-by":"crossref","unstructured":"Zhang S-y Liu Y-y Yang G-l EMD interval thresholding denoising based on correlation coefficient to select relevant modes. In: 2015 34th Chinese control conference (CCC) 2015 pp.4801\u20134806. IEEE.","DOI":"10.1109\/ChiCC.2015.7260382"},{"key":"e_1_3_4_22_2","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1998.0193"},{"key":"e_1_3_4_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2017.01.015"},{"key":"e_1_3_4_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2009.11.069"},{"key":"e_1_3_4_25_2","doi-asserted-by":"publisher","DOI":"10.1142\/S1793536909000047"},{"key":"e_1_3_4_26_2","doi-asserted-by":"crossref","unstructured":"Torres ME Colominas MA Schlotthauer G et al. A complete ensemble empirical mode decomposition with adaptive noise. In: 2011 IEEE international conference on acoustics speech and signal processing (ICASSP) 2011 pp.4144\u20134147. IEEE.","DOI":"10.1109\/ICASSP.2011.5947265"},{"key":"e_1_3_4_27_2","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2013.2288675"},{"key":"e_1_3_4_28_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2023.111007"},{"key":"e_1_3_4_29_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2019.105006"},{"key":"e_1_3_4_30_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijforecast.2015.11.015"},{"key":"e_1_3_4_31_2","doi-asserted-by":"publisher","DOI":"10.1175\/MWR2906.1"},{"key":"e_1_3_4_32_2","doi-asserted-by":"publisher","DOI":"10.1198\/jasa.2009.ap08615"},{"key":"e_1_3_4_33_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2004.02.003"},{"key":"e_1_3_4_34_2","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1997.9.8.1735"},{"key":"e_1_3_4_35_2","doi-asserted-by":"crossref","unstructured":"Karmiani D Kazi R Nambisan A et al. Comparison of predictive algorithms: Backpropagation SVM LSTM and Kalman Filter for stock market. In: 2019 amity international conference on artificial intelligence (AICAI) 2019 pp.228\u2013234. IEEE.","DOI":"10.1109\/AICAI.2019.8701258"},{"key":"e_1_3_4_36_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.12.008"},{"key":"e_1_3_4_37_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2021.115872"},{"issue":"3","key":"e_1_3_4_38_2","first-page":"\u00a040","article-title":"Bayesian analysis of mixture models with an unknown number of components-an alternative to reversible jump methods","volume":"28","author":"Stephens M","year":"2000","unstructured":"Stephens M. Bayesian analysis of mixture models with an unknown number of components-an alternative to reversible jump methods. Ann Stat 2000; 28(3):\u00a040\u201374.","journal-title":"Ann Stat"},{"key":"e_1_3_4_39_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.frl.2024.105364"},{"key":"e_1_3_4_40_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2016.03.017"},{"key":"e_1_3_4_41_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2014.11.019"},{"key":"e_1_3_4_42_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijforecast.2021.11.007"},{"key":"e_1_3_4_43_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0169-2070(96)00719-4"}],"container-title":["Intelligent Data Analysis: An International Journal"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1088467X241296754","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/1088467X241296754","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1088467X241296754","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:20:57Z","timestamp":1777454457000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/1088467X241296754"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12]]},"references-count":42,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,7]]}},"alternative-id":["10.1177\/1088467X241296754"],"URL":"https:\/\/doi.org\/10.1177\/1088467x241296754","relation":{},"ISSN":["1088-467X","1571-4128"],"issn-type":[{"value":"1088-467X","type":"print"},{"value":"1571-4128","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,12]]}}}