{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T20:12:17Z","timestamp":1791403937515,"version":"4.3.3"},"reference-count":31,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2009,9,30]],"date-time":"2009-09-30T00:00:00Z","timestamp":1254268800000},"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":[[2010,4]]},"abstract":"<jats:p>The paper discusses contemporaneous aggregation of the Linear ARCH (LARCH) model as defined in (1), which was introduced in Robinson (1991) and studied in Giraitis, Robinson, and Surgailis (2000) and other works. We show that the limiting aggregate of the (G)eneralized LARCH(1,1) process in (3)\u2013(4) with random Beta distributed coefficient <jats:italic>\u03b2<\/jats:italic> exhibits long memory. In particular, we prove that squares of the limiting aggregated process have slowly decaying correlations and their partial sums converge to a self-similar process of a new type.<\/jats:p>","DOI":"10.1017\/s026646660910004x","type":"journal-article","created":{"date-parts":[[2009,9,30]],"date-time":"2009-09-30T08:26:47Z","timestamp":1254299207000},"page":"406-425","source":"Crossref","is-referenced-by-count":15,"title":["AGGREGATION OF THE RANDOM COEFFICIENT GLARCH(1,1) PROCESS"],"prefix":"10.1017","volume":"26","author":[{"given":"Liudas","family":"Giraitis","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Remigijus","family":"Leipus","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Donatas","family":"Surgailis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2009,9,30]]},"reference":[{"key":"S026646660910004X_ref11","first-page":"70","volume-title":"Handbook of Financial Time Series","author":"Giraitis","year":"2009"},{"key":"S026646660910004X_ref7","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176995145"},{"key":"S026646660910004X_ref2","volume-title":"Higher Transcendental Functions","volume":"1","author":"Bateman","year":"1953"},{"key":"S026646660910004X_ref30","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2006.03.002"},{"key":"S026646660910004X_ref10","doi-asserted-by":"publisher","DOI":"10.1093\/jjfinec\/nbh008"},{"key":"S026646660910004X_ref18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2004.09.010"},{"key":"S026646660910004X_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(95)01737-2"},{"key":"S026646660910004X_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2004.08.014"},{"key":"S026646660910004X_ref27","doi-asserted-by":"publisher","DOI":"10.1007\/BF00535674"},{"key":"S026646660910004X_ref31","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.2006.00522.x"},{"key":"S026646660910004X_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2005.11.003"},{"key":"S026646660910004X_ref4","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1214\/aoap\/1050689598","article-title":"Asymptotic results for long memory LARCH sequences","volume":"13","author":"Berkes","year":"2003","journal-title":"Annals of Applied Probability"},{"key":"S026646660910004X_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2007.06.002"},{"key":"S026646660910004X_ref9","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600161018"},{"key":"S026646660910004X_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(02)00108-4"},{"key":"S026646660910004X_ref14","doi-asserted-by":"publisher","DOI":"10.2307\/20075720"},{"key":"S026646660910004X_ref15","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(80)90092-5"},{"key":"S026646660910004X_ref16","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(03)00209-4"},{"key":"S026646660910004X_ref1","volume-title":"Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables","author":"Abramowitz","year":"1972"},{"key":"S026646660910004X_ref17","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0425-1"},{"key":"S026646660910004X_ref19","doi-asserted-by":"publisher","DOI":"10.1023\/A:1015021801709"},{"key":"S026646660910004X_ref20","first-page":"185","volume-title":"Extreme Values in Finance, Telecommunications and the Environment","author":"Mikosch","year":"2003"},{"key":"S026646660910004X_ref23","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-3758(97)00149-3"},{"key":"S026646660910004X_ref22","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(91)90078-R"},{"key":"S026646660910004X_ref21","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.2004.01775.x"},{"key":"S026646660910004X_ref24","volume-title":"Almost Sure Convergence","author":"Stout","year":"1974"},{"key":"S026646660910004X_ref25","first-page":"185","article-title":"Zones of attraction of self-similar multiple integrals","volume":"22","author":"Surgailis","year":"1982","journal-title":"Lithuanian Mathematical Journal"},{"key":"S026646660910004X_ref26","first-page":"129","volume-title":"Long Range Dependence: Theory and Applications","author":"Surgailis","year":"2003"},{"key":"S026646660910004X_ref29","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(03)00207-0"},{"key":"S026646660910004X_ref12","doi-asserted-by":"crossref","first-page":"1002","DOI":"10.1214\/aoap\/1019487516","article-title":"A model for long memory conditional heteroskedasticity","volume":"10","author":"Giraitis","year":"2000","journal-title":"Annals of Applied Probability"},{"key":"S026646660910004X_ref28","first-page":"5","volume-title":"Long Range Dependence. 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