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Instead of using an iterative algorithm which is the standard practice for estimating CP-decompositions, we propose a new and one-pass estimation procedure based on a generalized eigenanalysis constructed from the serial dependence structure of the underlying process. To overcome the intricacy of solving a rank-reduced generalized eigenequation, we propose a further refined approach which projects it into a lower-dimensional full-ranked eigenequation. This refined method can significantly improve the finite-sample performance. We show that all the component coefficient vectors in the CP-decomposition can be estimated consistently. The proposed model and the estimation method are also illustrated with both simulated and real data, showing effective dimension-reduction in modelling and forecasting matrix time series.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkac011","type":"journal-article","created":{"date-parts":[[2023,1,28]],"date-time":"2023-01-28T09:06:37Z","timestamp":1674896797000},"page":"127-148","source":"Crossref","is-referenced-by-count":52,"title":["Modelling matrix time series via a tensor CP-decomposition"],"prefix":"10.1093","volume":"85","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7933-4449","authenticated-orcid":false,"given":"Jinyuan","family":"Chang","sequence":"first","affiliation":[{"name":"School of Statistics and Mathematics, Zhejiang Gongshang University , Hangzhou, Zhejiang , China"},{"name":"Joint Laboratory of Data Science and Business Intelligence, Southwestern University of Finance and Economics , Chengdu, Sichuan , China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jing","family":"He","sequence":"additional","affiliation":[{"name":"Joint Laboratory of Data Science and Business Intelligence, Southwestern University of Finance and Economics , Chengdu, Sichuan , China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lin","family":"Yang","sequence":"additional","affiliation":[{"name":"Joint Laboratory of Data Science and Business Intelligence, Southwestern University of Finance and Economics , Chengdu, Sichuan , China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2065-8486","authenticated-orcid":false,"given":"Qiwei","family":"Yao","sequence":"additional","affiliation":[{"name":"Department of Statistics, The London School of Economics and Political Science , London , 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