{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T22:26:23Z","timestamp":1772749583292,"version":"3.50.1"},"reference-count":34,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2009,2,11]],"date-time":"2009-02-11T00:00:00Z","timestamp":1234310400000},"content-version":"unspecified","delay-in-days":5124,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1995,2]]},"abstract":"<jats:p>This paper considers the properties of systems likelihood procedures for cointegrated systems when the I(2) variables are present. Two alternative methods are proposed: one is based on the full system likelihood, whereas another is based on the subsystem likelihood. By eliminating all unit roots in the system by the use of prior information concerning the presence of unit roots, these procedures yield estimates whose asymptotic distributions are mixed normal, free from nuisance parameters, and median-unbiased. Both methods are extensions of a full system maximum likelihood procedure by Phillips (1991a) to I(2) models. Three cases of cointegration with I(2) variables are considered in order to cover a wide variety of cointegration relationships. A triangular ECM representation and the two ML estimates are derived for each case, and the asymptotics are discussed as well. The asymptotic efficiency concerning the two estimates are considered.<\/jats:p>","DOI":"10.1017\/s0266466600009014","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T15:39:55Z","timestamp":1236699595000},"page":"1-24","source":"Crossref","is-referenced-by-count":15,"title":["Estimation of Cointegrated Systems with I(2) Processes"],"prefix":"10.1017","volume":"11","author":[{"given":"Yuichi","family":"Kitamura","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S0266466600009014_ref028","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176348666"},{"key":"S0266466600009014_ref032","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4149(83)90023-6"},{"key":"S0266466600009014_ref008","first-page":"71","article-title":"Multicointegration","volume":"8","author":"Granger","year":"1990","journal-title":"Advances in Econometrics"},{"key":"S0266466600009014_ref029","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600004217"},{"key":"S0266466600009014_ref030","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600007313"},{"key":"S0266466600009014_ref024","doi-asserted-by":"publisher","DOI":"10.2307\/2938258"},{"key":"S0266466600009014_ref023","first-page":"413","volume-title":"Nonparametric and Semiparametric Methods in Econometrics and Statistics","author":"Phillips","year":"1988"},{"key":"S0266466600009014_ref022","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600012287"},{"key":"S0266466600009014_ref005","doi-asserted-by":"publisher","DOI":"10.2307\/1425908"},{"key":"S0266466600009014_ref019","doi-asserted-by":"publisher","DOI":"10.2307\/2951679"},{"key":"S0266466600009014_ref004","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176344671"},{"key":"S0266466600009014_ref026","doi-asserted-by":"publisher","DOI":"10.2307\/2297545"},{"key":"S0266466600009014_ref027","doi-asserted-by":"publisher","DOI":"10.2307\/2298004"},{"key":"S0266466600009014_ref031","doi-asserted-by":"publisher","DOI":"10.2307\/2951763"},{"key":"S0266466600009014_ref001","first-page":"849","article-title":"Nested reduced rank autoregressive models for multiple time series","volume":"83","author":"Ahn","year":"1988","journal-title":"Journal of the American Statistical Association"},{"key":"S0266466600009014_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5505-5"},{"key":"S0266466600009014_ref020","unstructured":"Park J.Y. & Ogaki M. (1991) Seemingly Unrelated Canonical Cointegrating Regressions. Working paper 280, The Rochester Center for Economic Research."},{"key":"S0266466600009014_ref013","doi-asserted-by":"publisher","DOI":"10.1016\/0165-1889(88)90041-3"},{"key":"S0266466600009014_ref018","first-page":"819","article-title":"Stochastic trends and economic fluctuations","volume":"81","author":"King","year":"1991","journal-title":"American Economic Review"},{"key":"S0266466600009014_ref011","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176344793"},{"key":"S0266466600009014_ref016","volume-title":"A Statistical Analysis of Cointegration for 1(2) Variables","author":"Johansen","year":"1992"},{"key":"S0266466600009014_ref034","unstructured":"Yoo B.S. (1986) Multi\u2013Cointegrated Time Series and Generalized Error-Correction Models. USCD discussion paper."},{"key":"S0266466600009014_ref010","volume-title":"Martingale Limit Theory and Its Application.","author":"Hall","year":"1980"},{"key":"S0266466600009014_ref017","first-page":"383","article-title":"Production and inventory control at the General Motors Corporation during the 1920's and 193O's","volume":"83","author":"Kashyap","year":"1993","journal-title":"American Economic Review"},{"key":"S0266466600009014_ref012","doi-asserted-by":"publisher","DOI":"10.1017\/CCOL0521345529.002"},{"key":"S0266466600009014_ref021","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600013402"},{"key":"S0266466600009014_ref014","doi-asserted-by":"publisher","DOI":"10.2307\/2938278"},{"key":"S0266466600009014_ref009","volume-title":"Multivariate Regression Models with I(2)-Variables","author":"Haldrup","year":"1991"},{"key":"S0266466600009014_ref015","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600012755"},{"key":"S0266466600009014_ref006","doi-asserted-by":"publisher","DOI":"10.2307\/1913236"},{"key":"S0266466600009014_ref002","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1990.10474945"},{"key":"S0266466600009014_ref033","volume-title":"Statistical Analysis of Higher Order Integrated and Cointegrated Processes","author":"Tanaka","year":"1992"},{"key":"S0266466600009014_ref007","doi-asserted-by":"publisher","DOI":"10.2307\/1912172"},{"key":"S0266466600009014_ref025","unstructured":"Phillips P.C.B. (1991b) The Tail Behavior of Maximum Likelihood Estimators of Cointegrating Coefficients in Error Correction Models. Discussion paper 999, Cowles Foundation."}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466600009014","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,14]],"date-time":"2019-05-14T19:36:48Z","timestamp":1557862608000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466600009014\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,2]]},"references-count":34,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1995,2]]}},"alternative-id":["S0266466600009014"],"URL":"https:\/\/doi.org\/10.1017\/s0266466600009014","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,2]]}}}