{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T09:25:52Z","timestamp":1775899552009,"version":"3.50.1"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[1998,10,1]],"date-time":"1998-10-01T00:00:00Z","timestamp":907200000000},"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":[[1998,10]]},"abstract":"<jats:p>In this paper, we study the asymptotics of nonstationary \nfractional integrated time series, the long memory time \nseries with <jats:italic>d<\/jats:italic> \u2265 \u00bd, with special \nattention focused on the cases when <jats:italic>d<\/jats:italic> = \n(2<jats:italic>p<\/jats:italic> + 1)\/2 for integer <jats:italic>n<\/jats:italic> \nno less than 0. There is considerable empirical evidence showing \nlong memory of this magnitude in many economic time series including \nthe inflation rate and the stock market volatility. A study of the \nlarge-sample property is therefore both needed and useful. Also, we \nfound the asymptotics of nonstationary fractional integrated time \nseries useful in the study of the large-sample theory of the \nKwiatkowski\u2013Phillips\u2013Schmidt\u2013Shin test (1992, \n<jats:italic>Journal of Econometrics<\/jats:italic> 54, 159\u2013178).<\/jats:p>","DOI":"10.1017\/s026646669814505x","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T13:45:46Z","timestamp":1027777546000},"page":"641-662","source":"Crossref","is-referenced-by-count":14,"title":["ASYMPTOTICS OF NONSTATIONARY FRACTIONAL INTEGRATED SERIES"],"prefix":"10.1017","volume":"14","author":[{"given":"Ming","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[1998,10,1]]},"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S026646669814505X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,10]],"date-time":"2019-05-10T20:03:00Z","timestamp":1557518580000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S026646669814505X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,10]]},"references-count":0,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1998,10]]}},"alternative-id":["S026646669814505X"],"URL":"https:\/\/doi.org\/10.1017\/s026646669814505x","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,10]]}}}