{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,4]],"date-time":"2026-10-04T15:07:01Z","timestamp":1791126421087,"version":"4.1.0"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2000,2,1]],"date-time":"2000-02-01T00:00:00Z","timestamp":949363200000},"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":[[2000,2]]},"abstract":"<jats:p>This paper studies a broad class of nonnegative \nARCH(\u221e) models. Sufficient conditions for the existence \nof a stationary solution are established and an explicit \nrepresentation of the solution as a Volterra type series \nis found. Under our assumptions, the covariance function \ncan decay slowly like a power function, falling just short \nof the long memory structure. A moving average representation \nin martingale differences is established, and the central \nlimit theorem is proved.<\/jats:p>","DOI":"10.1017\/s0266466600161018","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T09:45:46Z","timestamp":1027763146000},"page":"3-22","source":"Crossref","is-referenced-by-count":182,"title":["STATIONARY ARCH MODELS: DEPENDENCE STRUCTURE AND CENTRAL \nLIMIT THEOREM"],"prefix":"10.1017","volume":"16","author":[{"given":"Liudas","family":"Giraitis","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Piotr","family":"Kokoszka","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Remigijus","family":"Leipus","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2000,2,1]]},"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466600161018","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,3]],"date-time":"2019-04-03T16:27:28Z","timestamp":1554308848000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466600161018\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,2]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2000,2]]}},"alternative-id":["S0266466600161018"],"URL":"https:\/\/doi.org\/10.1017\/s0266466600161018","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,2]]}}}