{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T15:32:56Z","timestamp":1772465576992,"version":"3.50.1"},"reference-count":55,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T00:00:00Z","timestamp":1772236800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["72101138"],"award-info":[{"award-number":["72101138"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["72301157"],"award-info":[{"award-number":["72301157"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Shandong Provincial Natural Science Foundation","doi-asserted-by":"publisher","award":["ZR2022QG036"],"award-info":[{"award-number":["ZR2022QG036"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Shandong Provincial Natural Science Foundation","doi-asserted-by":"publisher","award":["ZR2024MG003"],"award-info":[{"award-number":["ZR2024MG003"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Shandong Provincial Natural Science Foundation","doi-asserted-by":"publisher","award":["ZR2025MS1178"],"award-info":[{"award-number":["ZR2025MS1178"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Shandong Provincial Natural Science Foundation","doi-asserted-by":"publisher","award":["ZR2023QG122"],"award-info":[{"award-number":["ZR2023QG122"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Henan Philosophy and Social Science Program","award":["2023CJJ183"],"award-info":[{"award-number":["2023CJJ183"]}]},{"DOI":"10.13039\/501100018563","name":"Social Science Planning Project of Shandong Province","doi-asserted-by":"publisher","award":["22DJJJ24"],"award-info":[{"award-number":["22DJJJ24"]}],"id":[{"id":"10.13039\/501100018563","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100018563","name":"Social Science Planning Project of Shandong Province","doi-asserted-by":"publisher","award":["24DGLJ09"],"award-info":[{"award-number":["24DGLJ09"]}],"id":[{"id":"10.13039\/501100018563","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Shandong \u201c111\u201d Leading Talent Cultivation Program in Philosophy and Social Sciences, China"},{"name":"Shandong Province Higher Educational Youth Innovation Team Development Program"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>Accurate carbon price predictions are vital for supporting the effective functioning of the carbon market. Most existing studies rely on point-valued modeling, thus failing to fully explore interval-valued data and mixed-frequency information. To address this limitation, this paper proposes a new interval-valued carbon price forecasting paradigm and presents a mixed-frequency data-driven stacking ensemble forecasting system. The data preprocessing module in this system was designed to remove noise through signal decomposition and reconstruction. Additionally, the mixed-frequency modeling module integrates a mixed-frequency model, statistical model, and artificial intelligence model, which can fully utilize the significant potential of mixed-frequency information and overcome the limitations that result from selecting only one type of basic model. Moreover, a stacking ensemble learning module is proposed to fully exploit the advantages of the mixed-frequency modeling module, thereby providing more accurate forecasting results. Comparative experiments were performed and discussed based on the real carbon market, proving that the developed mixed-frequency data-driven stacking ensemble forecasting system outperforms other advanced methods and could provide an effective technique for improving carbon market management.<\/jats:p>","DOI":"10.3390\/systems14030255","type":"journal-article","created":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T14:06:56Z","timestamp":1772460416000},"page":"255","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A New Interval-Valued Carbon Price Forecasting Paradigm: Mixed-Frequency Data-Driven Stacking Ensemble Forecasting System"],"prefix":"10.3390","volume":"14","author":[{"given":"Yan","family":"Hao","sequence":"first","affiliation":[{"name":"Business School, Shandong Normal University, Jinan 250014, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingwen","family":"Zhang","sequence":"additional","affiliation":[{"name":"Business School, Shandong Normal University, Jinan 250014, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin","family":"Wang","sequence":"additional","affiliation":[{"name":"Business School, Shandong Normal University, Jinan 250014, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Liu","sequence":"additional","affiliation":[{"name":"Business School, Shandong Normal University, Jinan 250014, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6378-0732","authenticated-orcid":false,"given":"Wendong","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan 250014, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1016\/j.apenergy.2017.01.076","article-title":"Forecasting Carbon Price Using Empirical Mode Decomposition and Evolutionary Least Squares Support Vector Regression","volume":"191","author":"Zhu","year":"2017","journal-title":"Appl. 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