{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,4]],"date-time":"2026-10-04T04:34:31Z","timestamp":1791088471795,"version":"4.1.0"},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2008,4,4]],"date-time":"2008-04-04T00:00:00Z","timestamp":1207267200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2008,8]]},"abstract":"<jats:p>The question of which multivariate generalized autoregressive conditionally heteroskedastic (GARCH) models in the vec form are representable in the BEKK form is addressed. Using results from linear algebra, it is established that all vec models not representable in the simplest BEKK form contain matrices as parameters that map the vectorized positive semidefinite matrices into a strict subset of themselves. Moreover, a general result from linear algebra is presented implying that in dimension two the models are equivalent, and in dimension three a simple analytically tractable example for a vec model having no BEKK representation is given.<\/jats:p>","DOI":"10.1017\/s0266466608080456","type":"journal-article","created":{"date-parts":[[2008,4,4]],"date-time":"2008-04-04T05:51:43Z","timestamp":1207288303000},"page":"1131-1136","source":"Crossref","is-referenced-by-count":17,"title":["ON THE RELATION BETWEEN THE VEC AND BEKK MULTIVARIATE GARCH MODELS"],"prefix":"10.1017","volume":"24","author":[{"given":"Robert","family":"Stelzer","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2008,4,4]]},"reference":[{"key":"S0266466608080456_ref012","doi-asserted-by":"publisher","DOI":"10.1017\/S026646660707020X"},{"key":"S0266466608080456_ref011","unstructured":"Ribarits E.M. (2006) Multivariate modelling of financial time series. Ph.D. Thesis, Institute for Mathematical Methods in Economics, Vienna University of Technology, Vienna, Austria."},{"key":"S0266466608080456_ref010","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/03081089208818176","article-title":"A survey of linear preserver problems","volume":"33","author":"Pierce","year":"1992","journal-title":"Linear and Multilinear Algebra"},{"key":"S0266466608080456_ref009","doi-asserted-by":"publisher","DOI":"10.1080\/03081089208818179"},{"key":"S0266466608080456_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(75)90058-0"},{"key":"S0266466608080456_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(86)90063-1"},{"key":"S0266466608080456_ref013","doi-asserted-by":"publisher","DOI":"10.1007\/BF01397969"},{"key":"S0266466608080456_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2006.06.027"},{"key":"S0266466608080456_ref008","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-2003-022-3"},{"key":"S0266466608080456_ref001","doi-asserted-by":"publisher","DOI":"10.1002\/jae.842"},{"key":"S0266466608080456_ref007","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.2001.11919790"},{"key":"S0266466608080456_ref014","doi-asserted-by":"publisher","DOI":"10.1007\/BF02391860"},{"key":"S0266466608080456_ref003","unstructured":"Boussama F. (1998) Ergodicit\u00e9, m\u00e9lange et estimation dans les mod\u00e8les GARCH. Ph.D. Thesis, Universit\u00e9 Paris 7, Paris, France."},{"key":"S0266466608080456_ref006","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600009063"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466608080456","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,30]],"date-time":"2019-04-30T18:52:04Z","timestamp":1556650324000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466608080456\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,4,4]]},"references-count":14,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2008,8]]}},"alternative-id":["S0266466608080456"],"URL":"https:\/\/doi.org\/10.1017\/s0266466608080456","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,4,4]]}}}