{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T00:29:28Z","timestamp":1772756968995,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,1,13]],"date-time":"2022-01-13T00:00:00Z","timestamp":1642032000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11731015"],"award-info":[{"award-number":["11731015"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11701116"],"award-info":[{"award-number":["11701116"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Innovative Team Project of Ordinary Universities in Guangdong Province","award":["2020WCXTD018"],"award-info":[{"award-number":["2020WCXTD018"]}]},{"name":"Guangzhou University Research Fund","award":["YG2020029"],"award-info":[{"award-number":["YG2020029"]}]},{"name":"Guangzhou University Research Fund","award":["YH202108"],"award-info":[{"award-number":["YH202108"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Estimation of a conditional covariance matrix is an interesting and important research topic in statistics and econometrics. However, modelling ultra-high dimensional dynamic (conditional) covariance structures is known to suffer from the curse of dimensionality or the problem of singularity. To partially solve this problem, this paper establishes a model by combining the ideas of a factor model and a symmetric GARCH model to describe the dynamics of a high-dimensional conditional covariance matrix. Quasi maximum likelihood estimation (QMLE) and least square estimation (LSE) methods are used to estimate the parameters in the model, and the plug-in method is introduced to obtain the estimation of conditional covariance matrix. Asymptotic properties are established for the proposed method, and simulation studies are given to demonstrate its performance. A financial application is presented to support the methodology.<\/jats:p>","DOI":"10.3390\/sym14010158","type":"journal-article","created":{"date-parts":[[2022,1,14]],"date-time":"2022-01-14T03:14:56Z","timestamp":1642130096000},"page":"158","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["High-Dimensional Conditional Covariance Matrices Estimation Using a Factor-GARCH Model"],"prefix":"10.3390","volume":"14","author":[{"given":"Xiaoling","family":"Li","sequence":"first","affiliation":[{"name":"School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China"},{"name":"College of Mathematics and Informatics, South China Agricultural University, Guangzhou 510642, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xingfa","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuan","family":"Li","sequence":"additional","affiliation":[{"name":"School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1086\/261527","article-title":"A Capital Asset Pricing Model With Time-varying Covariances","volume":"96","author":"Bollerslev","year":"1988","journal-title":"J. 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