{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T20:01:17Z","timestamp":1791316877520,"version":"4.3.1"},"reference-count":29,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2017,10,17]],"date-time":"2017-10-17T00:00:00Z","timestamp":1508198400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["www.cambridge.org"],"crossmark-restriction":true},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2018,12]]},"abstract":"<jats:p>We prove the long standing conjecture of Ding and Granger (1996) about the existence of a stationary Long Memory ARCH model with finite fourth moment. This result follows from the necessary and sufficient conditions for the existence of covariance stationary integrated AR(\u221e), ARCH(\u221e), and FIGARCH models obtained in the present article. We also prove that such processes always have long memory.<\/jats:p>","DOI":"10.1017\/s0266466617000391","type":"journal-article","created":{"date-parts":[[2017,10,17]],"date-time":"2017-10-17T11:22:56Z","timestamp":1508239376000},"page":"1159-1179","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":7,"title":["STATIONARY INTEGRATED ARCH(\u221e) AND AR(\u221e) PROCESSES WITH FINITE VARIANCE"],"prefix":"10.1017","volume":"34","author":[{"given":"Liudas","family":"Giraitis","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Donatas","family":"Surgailis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andrius","family":"\u0160karnulis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2017,10,17]]},"reference":[{"key":"S0266466617000391_ref14","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/978-3-540-71297-8_3","volume-title":"Handbook of Financial Time Series","author":"Giraitis","year":"2009"},{"key":"S0266466617000391_ref5","doi-asserted-by":"crossref","unstructured":"Davidson, J . (2004) Moment and memory properties of linear conditional heteroscedasticity models, and a new model. Journal of Business & Economic Statistics 22, 16\u201329.","DOI":"10.1198\/073500103288619359"},{"key":"S0266466617000391_ref28","volume-title":"Real and Complex Analysis","author":"Rudin","year":"1987"},{"key":"S0266466617000391_ref1","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1017\/S0266466613000182","article-title":"Asymptotic normality for weighted sums of linear processes","volume":"30","author":"Abadir","year":"2014","journal-title":"Econometric Theory"},{"key":"S0266466617000391_ref25","first-page":"439","volume-title":"Theory and Applications of Long-Range Dependence","author":"Mikosch","year":"2003"},{"key":"S0266466617000391_ref22","unstructured":"Koulikov, D . (2003) Long memory ARCH(\u221e) models: Specification and quasi-maximum likelihood estimation. Working paper 163, Centre for Analytical Finance, Univ. Aarhus. 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