{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T16:57:13Z","timestamp":1781024233350,"version":"3.54.1"},"reference-count":59,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Applied Soft Computing"],"published-print":{"date-parts":[[2026,8]]},"DOI":"10.1016\/j.asoc.2026.115374","type":"journal-article","created":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T15:27:08Z","timestamp":1778081228000},"page":"115374","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["MTVformer: Multi-scale temporal-variable interaction network for long-term multivariate time series forecasting"],"prefix":"10.1016","volume":"200","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-5477-6060","authenticated-orcid":false,"given":"Xiaoman","family":"Yang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2349-2549","authenticated-orcid":false,"given":"Chang","family":"Wu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-8461-2388","authenticated-orcid":false,"given":"Yulin","family":"Xia","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-1086-1562","authenticated-orcid":false,"given":"Xinyi","family":"Du","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenchuan","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.asoc.2026.115374_bib0005","author":"Fulcher"},{"key":"10.1016\/j.asoc.2026.115374_bib0010","doi-asserted-by":"crossref","DOI":"10.1016\/j.asoc.2024.111365","article-title":"Stock price series forecasting using multi-scale modeling with boruta feature selection and adaptive denoising","volume":"154","author":"Li","year":"2024","journal-title":"Appl. Soft Comput."},{"key":"10.1016\/j.asoc.2026.115374_bib0015","doi-asserted-by":"crossref","DOI":"10.1016\/j.asoc.2023.110835","article-title":"Stock price forecasting using PSO hypertuned neural nets and ensembling","volume":"147","author":"Chauhan","year":"2023","journal-title":"Appl. Soft Comput."},{"key":"10.1016\/j.asoc.2026.115374_bib0020","doi-asserted-by":"crossref","DOI":"10.1016\/j.asoc.2024.112311","article-title":"A new framework for ultra-short-term electricity load forecasting model using IVMD\u2013SGMD two\u2013layer decomposition and INGO\u2013BiLSTM\u2013TPA\u2013TCN","volume":"167","author":"Cui","year":"2024","journal-title":"Appl. Soft Comput."},{"key":"10.1016\/j.asoc.2026.115374_bib0025","doi-asserted-by":"crossref","DOI":"10.1016\/j.asoc.2019.105994","article-title":"Short-term forecasting of renewable energy consumption: augmentation of a modified grey model with a Kalman filter","volume":"87","author":"Moonchai","year":"2020","journal-title":"Appl. Soft Comput."},{"key":"10.1016\/j.asoc.2026.115374_bib0030","doi-asserted-by":"crossref","DOI":"10.1016\/j.asoc.2023.110018","article-title":"Short-term electricity price forecasting based on similarity day screening, two-layer decomposition technique and Bi-LSTM neural network","volume":"136","author":"Wang","year":"2023","journal-title":"Appl. Soft Comput."},{"key":"10.1016\/j.asoc.2026.115374_bib0035","doi-asserted-by":"crossref","DOI":"10.1016\/j.asoc.2021.107857","article-title":"Aggregation of nonlinearly enhanced experts with application to electricity load forecasting","volume":"112","author":"Incremona","year":"2021","journal-title":"Appl. Soft Comput."},{"key":"10.1016\/j.asoc.2026.115374_bib0040","doi-asserted-by":"crossref","DOI":"10.1016\/j.asoc.2019.106029","article-title":"A novel system for multi-step electricity price forecasting for electricity market management","volume":"88","author":"Yang","year":"2020","journal-title":"Appl. Soft Comput."},{"key":"10.1016\/j.asoc.2026.115374_bib0045","doi-asserted-by":"crossref","DOI":"10.1016\/j.asoc.2024.111441","article-title":"Short-term global horizontal irradiance forecasting using weather classified categorical boosting","volume":"155","author":"Ahmed","year":"2024","journal-title":"Appl. Soft Comput."},{"key":"10.1016\/j.asoc.2026.115374_bib0050","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.neunet.2021.02.003","article-title":"A generative adversarial network approach to (ensemble) weather prediction","volume":"139","author":"Bihlo","year":"2021","journal-title":"Neural Netw."},{"key":"10.1016\/j.asoc.2026.115374_bib0055","doi-asserted-by":"crossref","DOI":"10.1016\/j.asoc.2025.112698","article-title":"Graph enhanced spatial\u2013temporal transformer for traffic flow forecasting","volume":"170","author":"Kong","year":"2025","journal-title":"Appl. Soft Comput."},{"key":"10.1016\/j.asoc.2026.115374_bib0060","doi-asserted-by":"crossref","DOI":"10.1016\/j.asoc.2025.112966","article-title":"Graph convolutional networks with multi-scale dynamics for traffic speed forecasting","volume":"174","author":"Zhang","year":"2025","journal-title":"Appl. Soft Comput."},{"key":"10.1016\/j.asoc.2026.115374_bib0065","doi-asserted-by":"crossref","DOI":"10.1016\/j.asoc.2022.109809","article-title":"Graph ensemble deep random vector functional link network for traffic forecasting","volume":"131","author":"Du","year":"2022","journal-title":"Appl. Soft Comput."},{"key":"10.1016\/j.asoc.2026.115374_bib0070","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.neucom.2020.11.026","article-title":"A temporal-aware LSTM enhanced by loss-switch mechanism for traffic flow forecasting","volume":"427","author":"Lu","year":"2021","journal-title":"Neurocomputing"},{"key":"10.1016\/j.asoc.2026.115374_bib0075","article-title":"Beverage manufacturing demand forecasting system driven by multi-stage machine learning model pool","author":"Shi","year":"2025","journal-title":"Appl. Soft Comput."},{"key":"10.1016\/j.asoc.2026.115374_bib0080","doi-asserted-by":"crossref","DOI":"10.1016\/j.asoc.2025.113274","article-title":"An adaptive multi-factor integrated forecasting model based on periodic reconstruction and random forest for carbon price","volume":"177","author":"Zhao","year":"2025","journal-title":"Appl. Soft Comput."},{"key":"10.1016\/j.asoc.2026.115374_bib0085","doi-asserted-by":"crossref","DOI":"10.1016\/j.neucom.2025.131103","article-title":"Deep-DFVAR: dynamic factor vector autoregression with deep learning for regional house price index forecasting","volume":"656","author":"Yeo","year":"2025","journal-title":"Neurocomputing"},{"key":"10.1016\/j.asoc.2026.115374_bib0090","series-title":"Advances in Neural Information Processing Systems","article-title":"Attention is all you need","volume":"vol. 30","author":"Vaswani","year":"2017"},{"key":"10.1016\/j.asoc.2026.115374_bib0095","series-title":"The Eleventh International Conference on Learning Representations","article-title":"A time series is worth 64 words: long-term forecasting with transformers","author":"Nie","year":"2023"},{"key":"10.1016\/j.asoc.2026.115374_bib0100","series-title":"The Twelfth International Conference on Learning Representations","article-title":"iTransformer: inverted transformers are effective for time series forecasting","author":"Liu","year":"2024"},{"key":"10.1016\/j.asoc.2026.115374_bib0105","series-title":"ICLR","article-title":"Pathformer: multi-scale transformers with adaptive pathways for time series forecasting","author":"Chen","year":"2024"},{"key":"10.1016\/j.asoc.2026.115374_bib0110","doi-asserted-by":"crossref","DOI":"10.1016\/j.inffus.2025.103398","article-title":"L3former: enhanced multi-scale shared transformer with local linear layer for long-term series forecasting","volume":"124","author":"Xia","year":"2025","journal-title":"Inf. Fusion"},{"key":"10.1016\/j.asoc.2026.115374_bib0115","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1109\/TAC.1972.1099963","article-title":"Time series analysis, forecasting and control","volume":"17","author":"Young","year":"1972","journal-title":"IEEE Trans. Autom. Control"},{"key":"10.1016\/j.asoc.2026.115374_bib0120","series-title":"Advances in Neural Information Processing Systems","article-title":"Induction of multiscale temporal structure","volume":"vol. 4","author":"Mozer","year":"1991"},{"key":"10.1016\/j.asoc.2026.115374_bib0125","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1214\/06-BA131","article-title":"Multi-scale and hidden resolution time series models","volume":"1","author":"Ferreira","year":"2006","journal-title":"Bayesian Anal."},{"key":"10.1016\/j.asoc.2026.115374_bib0130","article-title":"TSMixer: an All-MLP architecture for time series forecast-ing","author":"Chen","year":"2023","journal-title":"Trans. Mach. Learn. Res."},{"key":"10.1016\/j.asoc.2026.115374_bib0135","series-title":"The Twelfth International Conference on Learning Representations","article-title":"FITS: modeling time series with10kparameters","author":"Xu","year":"2024"},{"key":"10.1016\/j.asoc.2026.115374_bib0140","author":"Wang"},{"key":"10.1016\/j.asoc.2026.115374_bib0145","series-title":"2015 2nd International Conference on Pattern Recognition and Image Analysis (IPRIA)","first-page":"1","article-title":"An analytical review for event prediction system on time series","author":"Molaei","year":"2015"},{"key":"10.1016\/j.asoc.2026.115374_bib0150","series-title":"2018 International Conference on Network Infrastructure and Digital Content (IC-NIDC)","first-page":"431","article-title":"Research on feature engineering for time series data mining","author":"Li","year":"2018"},{"key":"10.1016\/j.asoc.2026.115374_bib0155","series-title":"2023 International Conference on Intelligent Systems for Communication, IoT and Security (ICISCoIS)","first-page":"538","article-title":"A comprehensive review on word embedding techniques","author":"Neelima","year":"2023"},{"key":"10.1016\/j.asoc.2026.115374_bib0160","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1109\/45.329294","article-title":"Feed-forward neural networks","volume":"13","author":"Bebis","year":"1994","journal-title":"IEEE Potentials"},{"key":"10.1016\/j.asoc.2026.115374_bib0165","series-title":"The Eleventh International Conference on Learning Representations","article-title":"Crossformer: transformer utilizing cross-dimension dependency for multivariate time series forecasting","author":"Zhang","year":"2023"},{"key":"10.1016\/j.asoc.2026.115374_bib0170","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1080\/13873954.2024.2416631","article-title":"An integrated approach for decomposing time series data into trend, cycle and seasonal components","volume":"30","author":"Kyo","year":"2024","journal-title":"Math. Comput. Model. Dyn. Syst."},{"key":"10.1016\/j.asoc.2026.115374_bib0175","first-page":"3","article-title":"STL: a seasonal-trend decomposition procedure based on loess","volume":"6","author":"Cleveland","year":"1990","journal-title":"J. Off. Stat."},{"key":"10.1016\/j.asoc.2026.115374_bib0180","series-title":"Advances in Neural Information Processing Systems","first-page":"22419","article-title":"Autoformer: decomposition transformers with auto-correlation for long-term series forecasting","volume":"vol. 34","author":"Wu","year":"2021"},{"key":"10.1016\/j.asoc.2026.115374_bib0185","series-title":"Proceedings of the 39th International Conference on Machine Learning","first-page":"27268","article-title":"FEDformer: frequency enhanced decomposed transformer for long-term series forecasting","volume":"vol. 162","author":"Zhou","year":"2022"},{"key":"10.1016\/j.asoc.2026.115374_bib0190","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1016\/j.csda.2013.09.010","article-title":"Dynamic seasonality in time series","volume":"70","author":"So","year":"2014","journal-title":"Comput. Stat. Data Anal."},{"key":"10.1016\/j.asoc.2026.115374_bib0195","doi-asserted-by":"crossref","first-page":"4550","DOI":"10.1016\/j.ins.2008.07.024","article-title":"Improving artificial neural networks\u2019 performance in seasonal time series forecasting","volume":"178","author":"Hamza\u00e7ebi","year":"2008","journal-title":"Inf. Sci."},{"key":"10.1016\/j.asoc.2026.115374_bib0200","series-title":"2019 International Conference on Signal Processing and Communication (ICSC)","first-page":"158","article-title":"Feature extraction: a survey of the types, techniques, applications","author":"Salau","year":"2019"},{"key":"10.1016\/j.asoc.2026.115374_bib0205","doi-asserted-by":"crossref","DOI":"10.1145\/2379776.2379788","article-title":"Time-series data mining","volume":"45","author":"Esling","year":"2012","journal-title":"ACM Comput. Surv."},{"key":"10.1016\/j.asoc.2026.115374_bib0210","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1038\/nature14539","article-title":"Deep learning","volume":"521","author":"LeCun","year":"2015","journal-title":"Nature"},{"key":"10.1016\/j.asoc.2026.115374_bib0215","doi-asserted-by":"crossref","first-page":"7129","DOI":"10.1109\/TKDE.2024.3400008","article-title":"The capacity and robustness trade-off: revisiting the channel independent strategy for multivariate time series forecasting","volume":"36","author":"Han","year":"2024","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"10.1016\/j.asoc.2026.115374_bib0220","series-title":"Forty-First International Conference on Machine Learning","article-title":"SAMformer: unlocking the potential of transformers in time series forecasting with sharpness-aware minimization and channel-wise attention","author":"Ilbert","year":"2024"},{"key":"10.1016\/j.asoc.2026.115374_bib0225","doi-asserted-by":"crossref","first-page":"14731","DOI":"10.1109\/ACCESS.2024.3357693","article-title":"Multi-scale transformer pyramid networks for multivariate time series forecasting","volume":"12","author":"Zhang","year":"2024","journal-title":"IEEE Access"},{"key":"10.1016\/j.asoc.2026.115374_bib0230","series-title":"Proceedings of the Thirty-Seventh AAAI Conference on Artificial Intelligence and Thirty-Fifth Conference on Innovative Applications of Artificial Intelligence and Thirteenth Symposium on Educational Advances in Artificial Intelligence","article-title":"NHITS: neural hierarchical interpolation for time series forecasting","author":"Challu","year":"2023"},{"key":"10.1016\/j.asoc.2026.115374_bib0235","series-title":"International Conference on Learning Representations","article-title":"MICN: multi-scale local and global context modeling for long-term series forecasting","author":"Wang","year":"2023"},{"key":"10.1016\/j.asoc.2026.115374_bib0240","series-title":"The Eleventh International Conference on Learning Representations","article-title":"TimesNet: temporal 2D-variation modeling for general time series analysis","author":"Wu","year":"2023"},{"key":"10.1016\/j.asoc.2026.115374_bib0245","author":"Fu"},{"key":"10.1016\/j.asoc.2026.115374_bib0250","series-title":"International Conference on Learning Representations","article-title":"Pyraformer: low-complexity pyramidal attention for long-range time series modeling and forecasting","author":"Liu","year":"2022"},{"key":"10.1016\/j.asoc.2026.115374_bib0255","series-title":"Advances in Neural Information Processing Systems","first-page":"5816","article-title":"SCINet: time series modeling and forecasting with sample convolution and interaction","volume":"vol. 35","author":"LIU","year":"2022"},{"key":"10.1016\/j.asoc.2026.115374_bib0260","author":"Adhikari"},{"key":"10.1016\/j.asoc.2026.115374_bib0265","series-title":"International Conference on Learning Representations","article-title":"Reversible instance normalization for accurate time-series forecasting against distribution shift","author":"Kim","year":"2022"},{"key":"10.1016\/j.asoc.2026.115374_bib0270","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1016\/j.ijforecast.2004.03.005","article-title":"The interaction between trend and seasonality","volume":"20","author":"Hyndman","year":"2004","journal-title":"Int. J. Forecast."},{"key":"10.1016\/j.asoc.2026.115374_bib0275","first-page":"11121","article-title":"Are transformers effective for time series forecasting?","volume":"37","author":"Zeng","year":"2023","journal-title":"Proc. AAAI Conf. Artif. Intell."},{"key":"10.1016\/j.asoc.2026.115374_bib0280","series-title":"Advances in Neural Information Processing Systems","first-page":"17723","article-title":"Long-short transformer: efficient transformers for language and vision","volume":"vol. 34","author":"Zhu","year":"2021"},{"key":"10.1016\/j.asoc.2026.115374_bib0285","series-title":"2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)","first-page":"770","article-title":"Deep residual learning for image recognition","author":"He","year":"2016"},{"key":"10.1016\/j.asoc.2026.115374_bib0290","series-title":"Advances in Neural Information Processing Systems","article-title":"PyTorch: an imperative style, high-performance deep learning library","volume":"vol. 32","author":"Paszke","year":"2019"},{"key":"10.1016\/j.asoc.2026.115374_bib0295","author":"Kingma"}],"container-title":["Applied Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1568494626008227?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1568494626008227?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T15:59:39Z","timestamp":1781020779000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1568494626008227"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8]]},"references-count":59,"alternative-id":["S1568494626008227"],"URL":"https:\/\/doi.org\/10.1016\/j.asoc.2026.115374","relation":{},"ISSN":["1568-4946"],"issn-type":[{"value":"1568-4946","type":"print"}],"subject":[],"published":{"date-parts":[[2026,8]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"MTVformer: Multi-scale temporal-variable interaction network for long-term multivariate time series forecasting","name":"articletitle","label":"Article Title"},{"value":"Applied Soft Computing","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.asoc.2026.115374","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Published by Elsevier B.V.","name":"copyright","label":"Copyright"}],"article-number":"115374"}}