{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T19:33:45Z","timestamp":1771011225188,"version":"3.50.1"},"reference-count":22,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2009,2,11]],"date-time":"2009-02-11T00:00:00Z","timestamp":1234310400000},"content-version":"unspecified","delay-in-days":6373,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1991,9]]},"abstract":"<jats:p>Some asymptotic properties of the least-squares estimator of the parameters of an AR model of order <jats:italic>p, p<\/jats:italic> \u2265 1, are studied when the roots of the characteristic polynomial of the given AR model are on or near the unit circle. Specifically, the convergence in distribution is established and the corresponding limiting random variables are represented in terms of functionals of suitable Brownian motions.<\/jats:p><jats:p>Further, the preceding convergence in distribution is strengthened to that of convergence uniformly over all Borel subsets. It is indicated that the method employed for this purpose has the potential of being applicable in the wider context of obtaining suitable asymptotic expansions of the distributions of leastsquares estimators.<\/jats:p>","DOI":"10.1017\/s0266466600004485","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T11:43:37Z","timestamp":1236685417000},"page":"269-306","source":"Crossref","is-referenced-by-count":50,"title":["On the Asymptotic Behavior of Least-Squares Estimators in AR Time Series with Roots Near the Unit Circle"],"prefix":"10.1017","volume":"7","author":[{"given":"P.","family":"Jeganathan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S0266466600004485_ref022","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177706450"},{"key":"S0266466600004485_ref017","first-page":"385","article-title":"On the least squares estimators for the unstable AR(2) models","author":"Nyblom","year":"1985","journal-title":"Bulletin of International Statistical Institute Contributed Paper Volume"},{"key":"S0266466600004485_ref008","volume-title":"Introduction to Statistical Time Series","author":"Fuller","year":"1976"},{"key":"S0266466600004485_ref003","volume-title":"Convergence of Probability Measures","author":"Billingsley","year":"1968"},{"key":"S0266466600004485_ref011","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176344793"},{"key":"S0266466600004485_ref005","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176350492"},{"key":"S0266466600004485_ref002","volume-title":"Normal Approximation and Asymptotic Expansions","author":"Bhattacharya","year":"1976"},{"key":"S0266466600004485_ref021","doi-asserted-by":"publisher","DOI":"10.1007\/BF00343897"},{"key":"S0266466600004485_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/BF01844607"},{"key":"S0266466600004485_ref019","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/74.3.535"},{"key":"S0266466600004485_ref016","volume-title":"Asymptotic Methods in Statistical Decision Theory","author":"LeCam","year":"1986"},{"key":"S0266466600004485_ref012","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176350962"},{"key":"S0266466600004485_ref013","unstructured":"13. 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University of Wisconsin, Madison."},{"key":"S0266466600004485_ref014","first-page":"1","article-title":"A note on martingale difference equations satisfying the local Marcinkeiwicz-Zygmund condition","volume":"11","author":"Lai","year":"1983","journal-title":"Bulletin of the Institute of Mathematics Academica Sinica"},{"key":"S0266466600004485_ref007","first-page":"427","article-title":"Distribution of the estimators for autoregressive time series with a unit root","volume":"74","author":"Dickey","year":"1979","journal-title":"Journal of American Statistical Association"},{"key":"S0266466600004485_ref018","doi-asserted-by":"publisher","DOI":"10.2307\/1913237"},{"key":"S0266466600004485_ref010","volume-title":"Martingale Limit Theory and Its Application","author":"Hall","year":"1980"},{"key":"S0266466600004485_ref004","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176350711"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466600004485","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,17]],"date-time":"2019-05-17T16:40:15Z","timestamp":1558111215000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466600004485\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,9]]},"references-count":22,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1991,9]]}},"alternative-id":["S0266466600004485"],"URL":"https:\/\/doi.org\/10.1017\/s0266466600004485","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,9]]}}}