{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,3]],"date-time":"2026-10-03T22:58:03Z","timestamp":1791068283691,"version":"4.1.0"},"reference-count":48,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2009,11,4]],"date-time":"2009-11-04T00:00:00Z","timestamp":1257292800000},"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":[[2010,8]]},"abstract":"<jats:p>For long memory time series models with uncorrelated but dependent errors, we establish the asymptotic normality of the Whittle estimator under mild conditions. Our framework includes the widely used fractional autoregressive integrated moving average models with generalized autoregressive conditional heteroskedastic-type innovations. To cover nonstationary fractionally integrated processes, we extend the idea of Abadir, Distaso, and Giraitis (2007,<jats:italic>Journal of Econometrics<\/jats:italic>141, 1353\u20131384) and develop the nonstationarity-extended Whittle estimation. The resulting estimator is shown to be asymptotically normal and is more efficient than the tapered Whittle estimator. Finally, the results from a small simulation study are presented to corroborate our theoretical findings.<\/jats:p>","DOI":"10.1017\/s0266466609990466","type":"journal-article","created":{"date-parts":[[2009,11,4]],"date-time":"2009-11-04T09:13:05Z","timestamp":1257325985000},"page":"1060-1087","source":"Crossref","is-referenced-by-count":26,"title":["NONSTATIONARITY-EXTENDED WHITTLE ESTIMATION"],"prefix":"10.1017","volume":"26","author":[{"given":"Xiaofeng","family":"Shao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2009,11,4]]},"reference":[{"key":"S0266466609990466_ref38","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466607070387"},{"key":"S0266466609990466_ref31","unstructured":"Phillips P.C.B . (1999) Discrete Fourier Transforms of Fractional Processes. Technical Report, Yale University."},{"key":"S0266466609990466_ref27","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466602183071"},{"key":"S0266466609990466_ref37","doi-asserted-by":"publisher","DOI":"10.1214\/009053606000001479"},{"key":"S0266466609990466_ref28","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-3758(98)00245-6"},{"key":"S0266466609990466_ref26","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1997.10474076"},{"key":"S0266466609990466_ref18","doi-asserted-by":"publisher","DOI":"10.1007\/BF00533484"},{"key":"S0266466609990466_ref16","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1214\/aos\/1018031107","article-title":"Whittle estimator for non-Gaussian long-memory time series","volume":"27","author":"Giraitis","year":"1999","journal-title":"Annals of Statistics"},{"key":"S0266466609990466_ref23","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176350257"},{"key":"S0266466609990466_ref30","doi-asserted-by":"publisher","DOI":"10.2307\/2938260"},{"key":"S0266466609990466_ref20","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008252331292"},{"key":"S0266466609990466_ref7","doi-asserted-by":"publisher","DOI":"10.1198\/073500103288619359"},{"key":"S0266466609990466_ref2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1099-1255(199601)11:1<23::AID-JAE374>3.0.CO;2-M"},{"key":"S0266466609990466_ref24","doi-asserted-by":"publisher","DOI":"10.1198\/016214506000001022"},{"key":"S0266466609990466_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2007.01.020"},{"key":"S0266466609990466_ref29","doi-asserted-by":"publisher","DOI":"10.1111\/j.1368-423X.2007.00202.x"},{"key":"S0266466609990466_ref21","doi-asserted-by":"publisher","DOI":"10.1002\/for.803"},{"key":"S0266466609990466_ref17","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.1989.tb00026.x"},{"key":"S0266466609990466_ref13","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466601173056"},{"key":"S0266466609990466_ref44","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700024137"},{"key":"S0266466609990466_ref48","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(03)00096-4"},{"key":"S0266466609990466_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-69395-8"},{"key":"S0266466609990466_ref3","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1111\/j.2517-6161.1995.tb02054.x","article-title":"Maximum likelihood estimation of the differencing parameter for invertible short and long memory autoregressive integrated moving average models","volume":"57","author":"Beran","year":"1995","journal-title":"Journal of the Royal Statistical Society, Series B"},{"key":"S0266466609990466_ref35","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780199257294.001.0001","volume-title":"Time Series with Long Memory","author":"Robinson","year":"2003"},{"key":"S0266466609990466_ref9","volume-title":"Theory and Applications of Long-Range Dependence","author":"Doukhan","year":"2003"},{"key":"S0266466609990466_ref22","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1214\/aos\/1034276623","article-title":"A limit theory for long-range dependence and statistical inference on related models","volume":"25","author":"Hosoya","year":"1997","journal-title":"Annals of Statistics"},{"key":"S0266466609990466_ref5","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176350963"},{"key":"S0266466609990466_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/0927-5398(93)90006-D"},{"key":"S0266466609990466_ref36","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2004.08.015"},{"key":"S0266466609990466_ref25","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1099-131X(199907)18:4<259::AID-FOR723>3.0.CO;2-7"},{"key":"S0266466609990466_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/BF01207515"},{"key":"S0266466609990466_ref10","doi-asserted-by":"publisher","DOI":"10.5194\/nhess-4-277-2004"},{"key":"S0266466609990466_ref6","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176347393"},{"key":"S0266466609990466_ref34","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176324317"},{"key":"S0266466609990466_ref4","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(86)90063-1"},{"key":"S0266466609990466_ref39","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2004.09.014"},{"key":"S0266466609990466_ref42","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198522249.001.0001","volume-title":"Non-linear Time Series: A Dynamical System Approach","author":"Tong","year":"1990"},{"key":"S0266466609990466_ref41","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/69.1.117"},{"key":"S0266466609990466_ref43","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2000.10474323"},{"key":"S0266466609990466_ref45","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0506715102"},{"key":"S0266466609990466_ref46","doi-asserted-by":"crossref","first-page":"939","DOI":"10.1016\/j.spa.2005.01.001","article-title":"On linear processes with dependent innovations","volume":"115","author":"Wu","year":"2005","journal-title":"Stochastic Processes and Their Applications"},{"key":"S0266466609990466_ref47","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1082999076"},{"key":"S0266466609990466_ref32","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1214\/009053604000000139","article-title":"Local Whittle estimation in nonstationary and unit root cases","volume":"32","author":"Phillips","year":"2004","journal-title":"Annals of Statistics"},{"key":"S0266466609990466_ref12","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176349936"},{"key":"S0266466609990466_ref40","volume-title":"An Introduction to Bispectral Analysis and Bilinear Time Series Models","author":"Subba Rao","year":"1984"},{"key":"S0266466609990466_ref33","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176324636"},{"key":"S0266466609990466_ref19","doi-asserted-by":"publisher","DOI":"10.2307\/3212501"},{"key":"S0266466609990466_ref15","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(02)00108-4"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466609990466","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,13]],"date-time":"2025-02-13T02:01:48Z","timestamp":1739412108000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466609990466\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,11,4]]},"references-count":48,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2010,8]]}},"alternative-id":["S0266466609990466"],"URL":"https:\/\/doi.org\/10.1017\/s0266466609990466","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,11,4]]}}}