{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,14]],"date-time":"2024-03-14T04:40:14Z","timestamp":1710391214837},"reference-count":21,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2009,10,1]],"date-time":"2009-10-01T00:00:00Z","timestamp":1254355200000},"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":[[2009,10]]},"abstract":"<jats:p>This paper investigates stationarity of the so-called integrated Markov-switching generalized autoregressive conditionally heteroskedastic (GARCH) process, which is an important subclass of the Markov-switching GARCH process introduced by Francq, Roussignol, and Zako\u00efan (2001,<jats:italic>Journal of Time Series Analysis<\/jats:italic>22,197\u2013220) and a Markov-switching version of the integrated GARCH (IGARCH) process. We show that, like the classical IGARCH process, a stationary solution with infinite variance for the integrated Markov-switching GARCH process may exist. To this purpose, an alternative condition for the existence of a strictly stationary solution of the Markov-switching GARCH process is presented, and some results obtained in Hennion (1997,<jats:italic>Annals of Probability<\/jats:italic>25, 1545\u20131587) are employed. In addition, we also discuss conditions for the existence of a strictly stationary solution of the Markov-switching GARCH process with finite variance, which is a modification of Theorem 2 in Francq et al. (2001).<\/jats:p>","DOI":"10.1017\/s0266466608090506","type":"journal-article","created":{"date-parts":[[2009,6,3]],"date-time":"2009-06-03T08:23:55Z","timestamp":1244017435000},"page":"1277-1288","source":"Crossref","is-referenced-by-count":4,"title":["INTEGRATED MARKOV-SWITCHING GARCH PROCESS"],"prefix":"10.1017","volume":"25","author":[{"given":"Ji-Chun","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,10,1]]},"reference":[{"key":"S0266466608090506_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/BF00532045"},{"key":"S0266466608090506_ref5","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9892.00219"},{"key":"S0266466608090506_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2005.04.005"},{"key":"S0266466608090506_ref4","doi-asserted-by":"publisher","DOI":"10.1080\/07474938608800095"},{"key":"S0266466608090506_ref18","doi-asserted-by":"publisher","DOI":"10.1162\/003465304323023886"},{"key":"S0266466608090506_ref14","doi-asserted-by":"publisher","DOI":"10.1093\/jjfinec\/nbl004"},{"key":"S0266466608090506_ref8","doi-asserted-by":"publisher","DOI":"10.1093\/jjfinec\/nbh020"},{"key":"S0266466608090506_ref17","doi-asserted-by":"crossref","first-page":"1427","DOI":"10.1214\/aos\/1015957401","article-title":"Limit theory for the sample autocorrelations and extremes of a GARCH(1,1) process","volume":"28","author":"Mikosch","year":"2000","journal-title":"Annals of Statistics"},{"key":"S0266466608090506_ref10","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1023481103"},{"key":"S0266466608090506_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/s001810100100"},{"key":"S0266466608090506_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/0304-405X(96)00875-6"},{"key":"S0266466608090506_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(92)90067-2"},{"key":"S0266466608090506_ref2","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176989526"},{"key":"S0266466608090506_ref3","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1080\/07350015.1994.10524546","article-title":"A Markov model of switching-regime ARCH","volume":"12","author":"Cai","year":"1994","journal-title":"Journal of Business and Economic Statistics"},{"key":"S0266466608090506_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(94)90067-1"},{"key":"S0266466608090506_ref12","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176996798"},{"key":"S0266466608090506_ref15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/07350015.1995.10524574","article-title":"Finite-sample properties of the maximum likelihood estimator in GARCH(1,1) and IGARCH(1,1) models: A Monte Carlo investigation","volume":"13","author":"Lumsdaine","year":"1995","journal-title":"Journal of Business and Economic Statistics"},{"key":"S0266466608090506_ref16","doi-asserted-by":"publisher","DOI":"10.2307\/2171862"},{"key":"S0266466608090506_ref19","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600005296"},{"key":"S0266466608090506_ref20","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1069362376"},{"key":"S0266466608090506_ref21","doi-asserted-by":"publisher","DOI":"10.1007\/0-387-32792-4"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466608090506","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,14]],"date-time":"2024-03-14T04:09:40Z","timestamp":1710389380000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466608090506\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,10]]},"references-count":21,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2009,10]]}},"alternative-id":["S0266466608090506"],"URL":"https:\/\/doi.org\/10.1017\/s0266466608090506","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,10]]}}}