{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T14:04:54Z","timestamp":1790777094541,"version":"4.1.0"},"reference-count":64,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T00:00:00Z","timestamp":1766707200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,4,14]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>We study the problem of factor modelling vector- and tensor-valued time series in the presence of heavy tails in the data, which produce extreme observations with nonnegligible probability. We propose combining a two-step procedure for tensor decomposition with data truncation, which is easy to implement and does not require an iterative search for a numerical solution. Departing from the light-tail assumptions often adopted in the time series factor-modelling literature, we derive the consistency and asymptotic normality of the proposed estimators while assuming the existence of the $ (2\\,+\\,2\\epsilon) $th moment only, for some $ \\epsilon\\in(0,1) $. Our rates explicitly depend on $ \\epsilon $, characterizing the effect of heavy tails and the chosen level of truncation. We also propose a consistent criterion for determining the number of factors. Simulation studies and applications to two macroeconomic datasets demonstrate the strong performance of the proposed estimators.<\/jats:p>","DOI":"10.1093\/biomet\/asaf093","type":"journal-article","created":{"date-parts":[[2025,12,19]],"date-time":"2025-12-19T12:58:52Z","timestamp":1766149132000},"source":"Crossref","is-referenced-by-count":3,"title":["Tail-robust factor modelling of vector and tensor time series in high dimensions"],"prefix":"10.1093","volume":"113","author":[{"given":"Matteo","family":"Barigozzi","sequence":"first","affiliation":[{"name":"Department of Economics, Universit\u00e0 di Bologna , Via Zamboni 33 , 40126 Bologna, \u00a0 matteo.barigozzi@unibo.it","place":["Italy"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0725-8704","authenticated-orcid":false,"given":"Haeran","family":"Cho","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of Bristol , Woodland Road , Bristol BS8 1UG,","place":["U.K"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hyeyoung","family":"Maeng","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Durham University , Stockton Road , Durham DH1 3LE, . hyeyoung.maeng@durham.ac.uk","place":["U.K"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2025,12,26]]},"reference":[{"key":"2026042200213797200_asaf093-B1","doi-asserted-by":"crossref","first-page":"1203","DOI":"10.3982\/ECTA8968","article-title":"Eigenvalue ratio test for the number of factors","volume":"81","author":"Ahn","year":"2013","journal-title":"Econometrica"},{"key":"2026042200213797200_asaf093-B2","doi-asserted-by":"crossref","first-page":"1806","DOI":"10.1016\/j.spl.2010.08.005","article-title":"Improved penalization for determining the number of factors in approximate static factor models","volume":"80","author":"Alessi","year":"2010","journal-title":"Statist. 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