{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T09:36:17Z","timestamp":1790069777601,"version":"4.0.1"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2001,2,7]],"date-time":"2001-02-07T00:00:00Z","timestamp":981504000000},"content-version":"unspecified","delay-in-days":6,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2001,2]]},"abstract":"<jats:p>This paper investigates the consistency of the least squares \nestimators and derives their limiting distributions in an AR(1) \nmodel with a single structural break of unknown timing. Let \n\u03b2<jats:sub>1<\/jats:sub> and \u03b2<jats:sub>2<\/jats:sub> be the preshift and \npostshift AR parameter, respectively. Three cases are considered: \n(i) |\u03b2<jats:sub>1<\/jats:sub>| &lt; 1 and \n|\u03b2<jats:sub>2<\/jats:sub>| &lt; 1; (ii) \n|\u03b2<jats:sub>1<\/jats:sub>| &lt; 1 and \u03b2<jats:sub>2<\/jats:sub> = 1; \nand (iii) \u03b2<jats:sub>1<\/jats:sub> = 1 and |\u03b2<jats:sub>2<\/jats:sub>| \n&lt; 1. Cases (ii) and (iii) are of particular interest but are rarely \ndiscussed in the literature. Surprising results are that, in both cases, regardless of the location of the change-point estimate, the unit root \ncan always be consistently estimated and the residual sum of squares \ndivided by the sample size converges to a <jats:italic>discontinuous<\/jats:italic> function \nof the change point. In case (iii), [circumflex over beta]<jats:sub>2<\/jats:sub> \ndoes not converge to \u03b2<jats:sub>2<\/jats:sub> whenever the change-point estimate \nis lower than the true change point. Further, the limiting distribution \nof the break-point estimator for shrinking break is asymmetric for case \n(ii), whereas those for cases (i) and (iii) are symmetric. The appropriate \nshrinking rate is found to be different in all cases.<\/jats:p>","DOI":"10.1017\/s0266466601171045","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T13:45:46Z","timestamp":1027777546000},"page":"87-155","source":"Crossref","is-referenced-by-count":61,"title":["STRUCTURAL CHANGE IN AR(1) MODELS"],"prefix":"10.1017","volume":"17","author":[{"given":"Terence Tai-Leung","family":"Chong","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2001,2,7]]},"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466601171045","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,9]],"date-time":"2019-04-09T20:10:28Z","timestamp":1554840628000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466601171045\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,2]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2001,2]]}},"alternative-id":["S0266466601171045"],"URL":"https:\/\/doi.org\/10.1017\/s0266466601171045","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,2]]}}}