{"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":1791088471450,"version":"4.1.0"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2002,5,15]],"date-time":"2002-05-15T00:00:00Z","timestamp":1021420800000},"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":[[2002,6]]},"abstract":"<jats:p>Although econometricians have been using Bollerslev's \n(1986, <jats:italic>Journal of Econometrics<\/jats:italic> 31, 307\u2013327) \nGARCH(<jats:italic>r<\/jats:italic>, <jats:italic>s<\/jats:italic>) model for over a decade, the higher \norder moment structure of the model remains unresolved. The sufficient \ncondition for the existence of the higher order moments of the \nGARCH(<jats:italic>r<\/jats:italic>, <jats:italic>s<\/jats:italic>) model was given by Ling (1999a, <jats:italic>Journal \nof Applied Probability<\/jats:italic> 36, 688\u2013705). This paper shows that \nLing's condition is also necessary. As an extension, the necessary \nand sufficient moment conditions are established for Ding, Granger, and \nEngle's (1993, <jats:italic>Journal of Empirical Finance<\/jats:italic>, 1, \n83\u2013106) asymmetric power GARCH(<jats:italic>r<\/jats:italic>, <jats:italic>s<\/jats:italic>) model.<\/jats:p>","DOI":"10.1017\/s0266466602183071","type":"journal-article","created":{"date-parts":[[2002,12,11]],"date-time":"2002-12-11T22:13:26Z","timestamp":1039644806000},"page":"722-729","source":"Crossref","is-referenced-by-count":200,"title":["NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE \nGARCH(<i>r<\/i>,<i>s<\/i>) AND ASYMMETRIC POWER \nGARCH(<i>r<\/i>,<i>s<\/i>) MODELS"],"prefix":"10.1017","volume":"18","author":[{"given":"Shiqing","family":"Ling","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"McAleer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2002,5,15]]},"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466602183071","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,4]],"date-time":"2019-04-04T19:50:53Z","timestamp":1554407453000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466602183071\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,5,15]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2002,6]]}},"alternative-id":["S0266466602183071"],"URL":"https:\/\/doi.org\/10.1017\/s0266466602183071","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,5,15]]}}}