{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T18:58:02Z","timestamp":1773082682219,"version":"3.50.1"},"reference-count":4,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2005,3,31]],"date-time":"2005-03-31T00:00:00Z","timestamp":1112227200000},"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":[[2005,4]]},"abstract":"<jats:p>This paper establishes various results involving functions of \nintegrated processes. Two theorems\u2014which improve similar results by \nPark and Phillips\u2014are proved for averages of functions of an \nintegrated process that has not been rescaled by the square root of sample \nsize. In addition, two results are given that characterize asymptotic \nbehavior of averages of nonintegrable functions of rescaled integrated \nprocesses; the observations close to the pole take over asymptotic \nbehavior in that case. Throughout, we make the assumption that the \ninnovations of the integrated process are a linear process.<\/jats:p>","DOI":"10.1017\/s026646660505022x","type":"journal-article","created":{"date-parts":[[2005,4,7]],"date-time":"2005-04-07T18:55:30Z","timestamp":1112900130000},"page":"413-430","source":"Crossref","is-referenced-by-count":21,"title":["FURTHER RESULTS ON THE ASYMPTOTICS FOR NONLINEAR TRANSFORMATIONS OF \nINTEGRATED TIME SERIES"],"prefix":"10.1017","volume":"21","author":[{"given":"Robert","family":"de Jong","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chien-Ho","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2005,3,31]]},"reference":[{"key":"S026646660505022X_ref001","doi-asserted-by":"crossref","unstructured":"Chung, K.L. & R.J. Williams (1990)Introduction to Stochastic Integration,2nd ed. Birkh\u00e4user.","DOI":"10.1007\/978-1-4612-4480-6"},{"key":"S026646660505022X_ref002","doi-asserted-by":"crossref","unstructured":"de Jong, R.M. (2004)Addendum to \u201cAsymptotics for nonlinear transformations ofintegrated time series.\u201d Econometric Theory(forthcoming).","DOI":"10.1017\/S0266466604203085"},{"key":"S026646660505022X_ref004","doi-asserted-by":"crossref","unstructured":"P\u00f6tscher, B.M. (2004)Nonlinear functions and convergence to Brownian motion: Beyond thecontinuous mapping theorem.Econometric Theory 20,1\u201322.","DOI":"10.1017\/S0266466604201013"},{"key":"S026646660505022X_ref003","doi-asserted-by":"crossref","unstructured":"Park, J.Y. & P.C.B. Phillips (1999)Asymptotics for nonlinear transformations of integrated timeseries.Econometric Theory 15,269\u2013298.","DOI":"10.1017\/S0266466699153015"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S026646660505022X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T22:24:40Z","timestamp":1750458280000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S026646660505022X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,3,31]]},"references-count":4,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2005,12]]}},"alternative-id":["S026646660505022X"],"URL":"https:\/\/doi.org\/10.1017\/s026646660505022x","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,3,31]]}}}