{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T20:54:45Z","timestamp":1773435285213,"version":"3.50.1"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2001,7,27]],"date-time":"2001-07-27T00:00:00Z","timestamp":996192000000},"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":[[2001,8]]},"abstract":"<jats:p>This paper considers nonstationary fractional autoregressive \nintegrated moving-average (<jats:italic>p<\/jats:italic>,<jats:italic>d<\/jats:italic>,<jats:italic>q<\/jats:italic>) models \nwith the fractionally differencing parameter <jats:italic>d<\/jats:italic> \u2208 \n(\u2212 1\/2,1\/2) and the autoregression function with roots on or \noutside the unit circle. Asymptotic inference is based on the \nconditional sum of squares (CSS) estimation. Under some suitable \nconditions, it is shown that CSS estimators exist and are consistent. \nThe asymptotic distributions of CSS estimators are expressed as \nfunctions of stochastic integrals of usual Brownian motions. Unlike \nresults available in the literature, the limiting distributions \nof various unit roots are independent of the parameter <jats:italic>d<\/jats:italic> over \nthe entire range <jats:italic>d<\/jats:italic> \u2208 (\u2212 1\/2,1\/2). This allows \nthe unit roots and <jats:italic>d<\/jats:italic> to be estimated and tested separately \nwithout loss of efficiency. Our results are quite different from the \ncurrent asymptotic theories on nonstationary long memory time series. \nThe finite sample properties are examined for two special cases through \nsimulations.<\/jats:p>","DOI":"10.1017\/s0266466601174049","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T13:16:52Z","timestamp":1027775812000},"page":"738-764","source":"Crossref","is-referenced-by-count":17,"title":["ASYMPTOTIC INFERENCE FOR NONSTATIONARY FRACTIONALLY \nINTEGRATED AUTOREGRESSIVE MOVING-AVERAGE MODELS"],"prefix":"10.1017","volume":"17","author":[{"given":"Shiqing","family":"Ling","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"W.K.","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2001,7,27]]},"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466601174049","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,8]],"date-time":"2019-04-08T19:21:14Z","timestamp":1554751274000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466601174049\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,7,27]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2001,8]]}},"alternative-id":["S0266466601174049"],"URL":"https:\/\/doi.org\/10.1017\/s0266466601174049","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,7,27]]}}}