{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T17:07:54Z","timestamp":1776877674506,"version":"3.51.2"},"reference-count":39,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"DOI":"10.13039\/501100013156","name":"Startup Foundation for Introducing Talent of Nanjing University of Information Science and Technology","doi-asserted-by":"publisher","award":["1513142501025"],"award-info":[{"award-number":["1513142501025"]}],"id":[{"id":"10.13039\/501100013156","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Uncert. Sys."],"published-print":{"date-parts":[[2026,6]]},"abstract":"<jats:p>Multivariate time series analysis is a crucial tool for examining the interdependence of multiple variables over time. Traditional probabilistic models require precise observational data. However, in practical applications, some variables are subject to inherent uncertainties that cannot be accurately quantified. To address this limitation, this paper introduces an uncertain vector autoregressive model with exogenous variables (UVARX) to incorporate uncertainty into multivariate time series analysis. The proposed model distinguishes between endogenous and exogenous variables, leveraging uncertainty theory to accommodate imprecise observations. A rigorous statistical framework\u00a0\u2014 encompassing parameter estimation, residual analysis, uncertain hypothesis test, cross-validation, and predictive evaluation\u00a0\u2014 is employed to validate the model. Empirical analysis on the joint forecasting of [Formula: see text] emissions and GDP, with electricity consumption as an exogenous factor, demonstrates the model\u2019s capability to handle imprecise data effectively. Results indicate that the UVARX model outperforms conventional approaches in forecasting accuracy, providing a robust analytical tool for uncertain multivariate time series. Since the transportation sector, particularly the automotive industry, is a major contributor to global [Formula: see text] emissions, the proposed methodology demonstrates strong potential for applications in intelligent vehicle systems and AI-driven energy management.<\/jats:p>","DOI":"10.1142\/s1752890925500229","type":"journal-article","created":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T03:00:39Z","timestamp":1761274839000},"source":"Crossref","is-referenced-by-count":2,"title":["Enhancing Multivariate Time Series Prediction: The UVARX Model for CO2 Emissions and Economic Growth"],"prefix":"10.1142","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8523-0080","authenticated-orcid":false,"given":"Han","family":"Tang","sequence":"first","affiliation":[{"name":"Beijing KOTEI AI Software Co., Ltd., Beijing 100083, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0298-5996","authenticated-orcid":false,"given":"Yuxing","family":"Jia","sequence":"additional","affiliation":[{"name":"School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7900-384X","authenticated-orcid":false,"given":"Yin","family":"Gao","sequence":"additional","affiliation":[{"name":"College of Science, Beijing Forestry University, Beijing 100872, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2025,11,12]]},"reference":[{"key":"S1752890925500229BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.eneco.2018.07.022"},{"key":"S1752890925500229BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/s10668-021-01579-7"},{"key":"S1752890925500229BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijforecast.2014.08.013"},{"key":"S1752890925500229BIB004","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-201724"},{"key":"S1752890925500229BIB005","doi-asserted-by":"publisher","DOI":"10.1142\/S0218488521500033"},{"key":"S1752890925500229BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.eap.2023.05.022"},{"issue":"2","key":"S1752890925500229BIB007","first-page":"763","volume":"7","author":"Dowell J.","year":"2015","journal-title":"IEEE Trans. Smart Grid"},{"key":"S1752890925500229BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.renene.2021.10.066"},{"key":"S1752890925500229BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.heliyon.2023.e12858"},{"key":"S1752890925500229BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/s11356-022-19097-y"},{"key":"S1752890925500229BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/j.rser.2023.113500"},{"key":"S1752890925500229BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2020.110189"},{"key":"S1752890925500229BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-73165-8_5"},{"issue":"1","key":"S1752890925500229BIB014","first-page":"3","volume":"2","author":"Liu B.","year":"2008","journal-title":"J. Uncertain Syst."},{"key":"S1752890925500229BIB015","doi-asserted-by":"publisher","DOI":"10.1186\/2195-5468-1-1"},{"key":"S1752890925500229BIB016","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-44354-5"},{"key":"S1752890925500229BIB017","doi-asserted-by":"publisher","DOI":"10.1080\/03610918.2020.1747077"},{"key":"S1752890925500229BIB018","doi-asserted-by":"publisher","DOI":"10.1016\/j.rser.2016.10.058"},{"key":"S1752890925500229BIB019","doi-asserted-by":"publisher","DOI":"10.1016\/j.energy.2019.03.126"},{"key":"S1752890925500229BIB020","doi-asserted-by":"publisher","DOI":"10.1016\/j.apenergy.2021.117223"},{"key":"S1752890925500229BIB021","doi-asserted-by":"publisher","DOI":"10.1016\/j.jenvman.2019.109742"},{"key":"S1752890925500229BIB022","doi-asserted-by":"publisher","DOI":"10.2307\/1912017"},{"key":"S1752890925500229BIB023","doi-asserted-by":"publisher","DOI":"10.1198\/016214502388618960"},{"key":"S1752890925500229BIB024","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3261-0"},{"key":"S1752890925500229BIB025","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-020-04991-9"},{"key":"S1752890925500229BIB026","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-210848"},{"key":"S1752890925500229BIB027","doi-asserted-by":"publisher","DOI":"10.1080\/03610926.2021.1906433"},{"key":"S1752890925500229BIB028","doi-asserted-by":"publisher","DOI":"10.1007\/s11356-022-18805-y"},{"key":"S1752890925500229BIB029","doi-asserted-by":"publisher","DOI":"10.1016\/j.jclepro.2018.09.034"},{"key":"S1752890925500229BIB030","doi-asserted-by":"publisher","DOI":"10.1016\/j.jclepro.2016.12.159"},{"issue":"1","key":"S1752890925500229BIB031","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/03081079.2020.1832485","volume":"50","author":"Xin Y.","year":"2021","journal-title":"Int. J. Gen. Syst."},{"key":"S1752890925500229BIB032","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-024-09421-1"},{"key":"S1752890925500229BIB033","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-018-9298-z"},{"key":"S1752890925500229BIB034","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-020-05079-0"},{"key":"S1752890925500229BIB035","doi-asserted-by":"publisher","DOI":"10.1080\/03610926.2020.1713373"},{"key":"S1752890925500229BIB036","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-021-09365-w"},{"key":"S1752890925500229BIB037","doi-asserted-by":"publisher","DOI":"10.1142\/S0218488520500415"},{"key":"S1752890925500229BIB038","doi-asserted-by":"publisher","DOI":"10.1016\/j.scitotenv.2020.136649"},{"key":"S1752890925500229BIB039","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-024-09419-9"}],"container-title":["Journal of Uncertain Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1752890925500229","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T02:49:54Z","timestamp":1768877394000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1752890925500229"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,12]]},"references-count":39,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2026,6]]}},"alternative-id":["10.1142\/S1752890925500229"],"URL":"https:\/\/doi.org\/10.1142\/s1752890925500229","relation":{},"ISSN":["1752-8909","1752-8917"],"issn-type":[{"value":"1752-8909","type":"print"},{"value":"1752-8917","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,12]]},"article-number":"2550022"}}