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In this paper, we present a factor model approach, in a form similar to tensor CANDECOMP\/PARAFAC (CP) decomposition, to the analysis of high-dimensional dynamic tensor time series. As the loading vectors are uniquely defined but not necessarily orthogonal, it is significantly different from the existing tensor factor models based on Tucker-type tensor decomposition. The model structure allows for a set of uncorrelated one-dimensional latent dynamic factor processes, making it much more convenient to study the underlying dynamics of the time series. A new high-order projection estimator is proposed for such a factor model, utilizing the special structure and the idea of the higher order orthogonal iteration procedures commonly used in Tucker-type tensor factor model and general tensor CP decomposition procedures. Theoretical investigation provides statistical error bounds for the proposed methods, which shows the significant advantage of utilizing the special model structure. Simulation study is conducted to further demonstrate the finite sample properties of the estimators. Real data application is used to illustrate the model and its interpretations.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkae036","type":"journal-article","created":{"date-parts":[[2024,5,16]],"date-time":"2024-05-16T17:26:32Z","timestamp":1715880392000},"page":"1383-1413","source":"Crossref","is-referenced-by-count":25,"title":["CP factor model for dynamic tensors"],"prefix":"10.1093","volume":"86","author":[{"given":"Yuefeng","family":"Han","sequence":"first","affiliation":[{"name":"Department of Applied and Computational Mathematics and Statistics, University of Notre Dame , Notre Dame, IN 46556 ,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dan","family":"Yang","sequence":"additional","affiliation":[{"name":"Faculty of Business and Economics, The University of Hong Kong , Pokfulam ,","place":["Hong Kong"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cun-Hui","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department 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