{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,4]],"date-time":"2026-10-04T04:34:32Z","timestamp":1791088472246,"version":"4.1.0"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[1999,12,1]],"date-time":"1999-12-01T00:00:00Z","timestamp":944006400000},"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":[[1999,12]]},"abstract":"<jats:p>\n                    In this paper, a necessary and sufficient condition \nfor the existence of the unconditional fourth moment of \nthe GARCH(\n                    <jats:italic>p<\/jats:italic>\n                    ,\n                    <jats:italic>q<\/jats:italic>\n                    ) process is given and \nalso an expression for the moment itself. Furthermore, \nthe autocorrelation function of the centered and squared \nobservations of this process is derived. The statistical \ntheory is further illustrated by a few special cases such \nas the GARCH(2,2) process and the ARCH(\n                    <jats:italic>q<\/jats:italic>\n                    ) process.\n                  <\/jats:p>","DOI":"10.1017\/s0266466699156032","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T09:45:46Z","timestamp":1027763146000},"page":"824-846","source":"Crossref","is-referenced-by-count":87,"title":["FOURTH MOMENT STRUCTURE OF THE GARCH(\n                    <i>p<\/i>\n                    ,\n                    <i>q<\/i>\n                    ) PROCESS"],"prefix":"10.1017","volume":"15","author":[{"given":"Changli","family":"He","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Timo","family":"Ter\u00e4svirta","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[1999,12,1]]},"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466699156032","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,9]],"date-time":"2019-05-09T15:42:46Z","timestamp":1557416566000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466699156032\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,12]]},"references-count":0,"journal-issue":{"issue":"6","published-print":{"date-parts":[[1999,12]]}},"alternative-id":["S0266466699156032"],"URL":"https:\/\/doi.org\/10.1017\/s0266466699156032","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,12]]}}}