{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,26]],"date-time":"2026-09-26T09:20:34Z","timestamp":1790414434824,"version":"4.1.0"},"reference-count":50,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2009,4,1]],"date-time":"2009-04-01T00:00:00Z","timestamp":1238544000000},"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":[[2009,4]]},"abstract":"<jats:p>This paper investigates the asymptotic theory for a factor GARCH (generalized autoregressive conditional heteroskedasticity) model. Sufficient conditions for asymptotic stability and existence of moments are established. These conditions allow for volatility spillover and integrated GARCH. We then show the strong consistency and asymptotic normality of the quasi\u2013maximum likelihood estimator (QMLE) of the model parameters. The results are obtained under the finiteness of the fourth-order moment of the innovations.<\/jats:p>","DOI":"10.1017\/s0266466608090117","type":"journal-article","created":{"date-parts":[[2009,1,29]],"date-time":"2009-01-29T09:18:26Z","timestamp":1233220706000},"page":"336-363","source":"Crossref","is-referenced-by-count":40,"title":["ASYMPTOTIC THEORY FOR A FACTOR GARCH MODEL"],"prefix":"10.1017","volume":"25","author":[{"given":"Christian M.","family":"Hafner","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arie","family":"Preminger","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2009,4,1]]},"reference":[{"key":"S0266466608090117_ref14","doi-asserted-by":"publisher","DOI":"10.1002\/jae.717"},{"key":"S0266466608090117_ref48","doi-asserted-by":"publisher","DOI":"10.1002\/jae.688"},{"key":"S0266466608090117_ref20","doi-asserted-by":"publisher","DOI":"10.1198\/073500102288618487"},{"key":"S0266466608090117_ref44","volume-title":"A GARCH(1,1) Estimate with (almost) No Moment Conditions on the Error Term","author":"Preminger","year":"2006"},{"key":"S0266466608090117_ref42","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600005296"},{"key":"S0266466608090117_ref40","unstructured":"Meitz M. & Saikkonen P. (2004) Ergodicity, Mixing and Existence of Moments of a Class of Markov Models with Applications to GARCH and ACD Models. Working Paper Series in Economics and Finance, Stockholm School of Economics."},{"key":"S0266466608090117_ref26","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0086655"},{"key":"S0266466608090117_ref29","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466607070119"},{"key":"S0266466608090117_ref50","volume-title":"Asymptotic Theory for Econometricians","author":"White","year":"2001"},{"key":"S0266466608090117_ref10","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176989526"},{"key":"S0266466608090117_ref36","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600008215"},{"key":"S0266466608090117_ref8","doi-asserted-by":"publisher","DOI":"10.1086\/261527"},{"key":"S0266466608090117_ref17","doi-asserted-by":"publisher","DOI":"10.1016\/S0047-259X(02)00009-X"},{"key":"S0266466608090117_ref38","doi-asserted-by":"publisher","DOI":"10.2307\/2171862"},{"key":"S0266466608090117_ref6","doi-asserted-by":"publisher","DOI":"10.2307\/2109358"},{"key":"S0266466608090117_ref3","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9892.00245"},{"key":"S0266466608090117_ref9","doi-asserted-by":"publisher","DOI":"10.1080\/07474939208800229"},{"key":"S0266466608090117_ref28","doi-asserted-by":"publisher","DOI":"10.1093\/jjfinec\/nbg001"},{"key":"S0266466608090117_ref22","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(90)90099-F"},{"key":"S0266466608090117_ref13","first-page":"81","article-title":"Asymptotic normality for the quasi-maximum likelihood estimator of a GARCH model","volume":"331","author":"Boussama","year":"2000","journal-title":"Comptes Rendus de l'Acad\u00e9mie des Sciences de Paris"},{"key":"S0266466608090117_ref45","doi-asserted-by":"publisher","DOI":"10.2307\/1425967"},{"key":"S0266466608090117_ref27","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1860-9"},{"key":"S0266466608090117_ref15","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466602181023"},{"key":"S0266466608090117_ref12","unstructured":"Boussama F . (1998) Ergodicity, mixing and estimation in GARCH models. Ph.D. Dissertation, University Paris 7."},{"key":"S0266466608090117_ref18","first-page":"313","article-title":"Mixing conditions for Markov chains","volume":"18","author":"Davydov","year":"1973","journal-title":"Theory of Probability and Its Applications"},{"key":"S0266466608090117_ref41","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-3267-7"},{"key":"S0266466608090117_ref4","doi-asserted-by":"publisher","DOI":"10.1002\/jae.842"},{"key":"S0266466608090117_ref43","doi-asserted-by":"publisher","DOI":"10.1007\/BF02613654"},{"key":"S0266466608090117_ref33","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466606060142"},{"key":"S0266466608090117_ref46","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2005.11.020"},{"key":"S0266466608090117_ref35","doi-asserted-by":"publisher","DOI":"10.1198\/073500106000000404"},{"key":"S0266466608090117_ref2","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00082"},{"key":"S0266466608090117_ref16","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9892.00197"},{"key":"S0266466608090117_ref5","doi-asserted-by":"publisher","DOI":"10.3150\/bj\/1068128975"},{"key":"S0266466608090117_ref49","doi-asserted-by":"publisher","DOI":"10.1111\/1368-423X.t01-1-00111"},{"key":"S0266466608090117_ref23","doi-asserted-by":"publisher","DOI":"10.3150\/bj\/1093265632"},{"key":"S0266466608090117_ref24","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466606060373"},{"key":"S0266466608090117_ref30","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466698141038"},{"key":"S0266466608090117_ref21","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600009063"},{"key":"S0266466608090117_ref25","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2007.01.001"},{"key":"S0266466608090117_ref31","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176996798"},{"key":"S0266466608090117_ref34","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466605050474"},{"key":"S0266466608090117_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(92)90067-2"},{"key":"S0266466608090117_ref37","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466603192092"},{"key":"S0266466608090117_ref47","doi-asserted-by":"publisher","DOI":"10.1198\/073500102288618496"},{"key":"S0266466608090117_ref39","volume-title":"Handbook of Matrices","author":"L\u00fctkepohl","year":"1996"},{"key":"S0266466608090117_ref32","unstructured":"Kristensen D . (2007) Geometric Ergodicity of a Class of Markov Chains with Applications to Time Series Models. Working paper, University of Wisconsin."},{"key":"S0266466608090117_ref19","doi-asserted-by":"crossref","first-page":"786","DOI":"10.1214\/aos\/1031833674","article-title":"Adaptive estimation in time series models","volume":"25","author":"Drost","year":"1997","journal-title":"Annals of Statistics"},{"key":"S0266466608090117_ref1","first-page":"21","volume-title":"Mastering Risk","volume":"vol. II","author":"Alexander","year":"2001"},{"key":"S0266466608090117_ref7","doi-asserted-by":"publisher","DOI":"10.2307\/2951782"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466608090117","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,8]],"date-time":"2019-04-08T20:31:24Z","timestamp":1554755484000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466608090117\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,4]]},"references-count":50,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2009,4]]}},"alternative-id":["S0266466608090117"],"URL":"https:\/\/doi.org\/10.1017\/s0266466608090117","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,4]]}}}