{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,11]],"date-time":"2026-01-11T00:33:59Z","timestamp":1768091639482,"version":"3.49.0"},"reference-count":49,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2016,12,20]],"date-time":"2016-12-20T00:00:00Z","timestamp":1482192000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"The National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71540027"],"award-info":[{"award-number":["71540027"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"The National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71671135"],"award-info":[{"award-number":["71671135"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"The National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51479151"],"award-info":[{"award-number":["51479151"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"The National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61403288"],"award-info":[{"award-number":["61403288"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013286","name":"Specialized Research Fund for the Doctoral Program of Higher Education of China","doi-asserted-by":"publisher","award":["20120143110001"],"award-info":[{"award-number":["20120143110001"]}],"id":[{"id":"10.13039\/501100013286","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Pingdingshan university key disciplines \u2018Applied Mathematics\u2019","award":["2016062"],"award-info":[{"award-number":["2016062"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper studies the grey coupled prediction problem of traffic data with panel data characteristics. Traffic flow data collected continuously at the same site typically has panel data characteristics. The longitudinal data (daily flow) is time-series data, which show an obvious intra-day trend and can be predicted using the autoregressive integrated moving average (ARIMA) model. The cross-sectional data is composed of observations at the same time intervals on different days and shows weekly seasonality and limited data characteristics; this data can be predicted using the rolling seasonal grey model (RSDGM(1,1)). The length of the rolling sequence is determined using matrix perturbation analysis. Then, a coupled model is established based on the ARIMA and RSDGM(1,1) models; the coupled prediction is achieved at the intersection of the time-series data and cross-sectional data, and the weights are determined using grey relational analysis. Finally, numerical experiments on 16 groups of cross-sectional data show that the RSDGM(1,1) model has good adaptability and stability and can effectively predict changes in traffic flow. The performance of the coupled model is also better than that of the benchmark model, the coupled model with equal weights and the Bayesian combination model.<\/jats:p>","DOI":"10.3390\/e18120454","type":"journal-article","created":{"date-parts":[[2016,12,23]],"date-time":"2016-12-23T04:09:09Z","timestamp":1482466149000},"page":"454","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Grey Coupled Prediction Model for Traffic Flow with Panel Data Characteristics"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8714-3220","authenticated-orcid":false,"given":"Jinwei","family":"Yang","sequence":"first","affiliation":[{"name":"College of Science, Wuhan University of Technology, Wuhan 430063, China"},{"name":"School of mathematics and statistics, Pingdingshan University, Pingdingshan 467000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinping","family":"Xiao","sequence":"additional","affiliation":[{"name":"College of Science, Wuhan University of Technology, Wuhan 430063, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuhua","family":"Mao","sequence":"additional","affiliation":[{"name":"College of Science, Wuhan University of Technology, Wuhan 430063, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Congjun","family":"Rao","sequence":"additional","affiliation":[{"name":"College of Science, Wuhan University of Technology, Wuhan 430063, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianghui","family":"Wen","sequence":"additional","affiliation":[{"name":"College of Science, Wuhan University of Technology, Wuhan 430063, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,12,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.trc.2014.01.005","article-title":"Short-term traffic forecasting: Where we are and where we\u2019re going","volume":"43","author":"Vlahogianni","year":"2014","journal-title":"Transp. 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