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Our primary goal is to identify and estimate the factor loadings in the CP decomposition. We propose a one-pass estimation procedure through standard eigen-analysis for a matrix constructed based on the serial dependence structure of the data. The asymptotic properties of the proposed estimator are established under a general setting as long as the factor loading vectors are linearly independent, allowing the factors to be correlated and the factor loading vectors to be not nearly orthogonal. The procedure adapts to the sparsity of the factor loading vectors, accommodates weak factors, and demonstrates strong performance across a wide range of scenarios. To further reduce estimation errors, we also introduce an iterative algorithm based on a novel double projection approach. We theoretically justify the improved convergence rate of the iterative estimator, and derive the associated limiting distribution. A consistent estimator of the asymptotic variance is also provided, which plays a key role in the related inference problems. All results are validated through extensive simulations and two real data applications.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkag125","type":"journal-article","created":{"date-parts":[[2026,9,4]],"date-time":"2026-09-04T11:35:12Z","timestamp":1788521712000},"source":"Crossref","is-referenced-by-count":1,"title":["CP-factorization for high-dimensional tensor time series and double projection iterations"],"prefix":"10.1093","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7933-4449","authenticated-orcid":false,"given":"Jinyuan","family":"Chang","sequence":"first","affiliation":[{"name":"Joint Laboratory of Data Science and Business Intelligence, Institute of Statistical Interdisciplinary Research, Southwestern University of Finance and Economics , Chengdu ,","place":["China"]},{"name":"State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences , Beijing ,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guanglin","family":"Huang","sequence":"additional","affiliation":[{"name":"Joint Laboratory of Data Science and Business Intelligence, Institute of Statistical Interdisciplinary Research, Southwestern University of Finance and Economics , Chengdu ,","place":["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 ,","place":["UK"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7666-6840","authenticated-orcid":false,"given":"Long","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Statistics and Data Science, Institute of Data Science and Statistics, Shanghai University of Finance and 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