{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T13:27:25Z","timestamp":1776778045996,"version":"3.51.2"},"reference-count":45,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,12,4]],"date-time":"2014-12-04T00:00:00Z","timestamp":1417651200000},"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":[[2016,4]]},"abstract":"<jats:p>This paper develops an asymptotic theory for estimated change-points in linear and nonlinear time series models. Based on a measurable objective function, it is shown that the estimated change-point converges weakly to the location of the maxima of a double-sided random walk and other estimated parameters are asymptotically normal. When the magnitude<jats:italic>d<\/jats:italic>of changed parameters is small, it is shown that the limiting distribution can be approximated by the known distribution as in Yao (1987,<jats:italic>Annals of Statistics<\/jats:italic>15, 1321\u20131328). This provides a channel to connect our results with those in Picard (1985,<jats:italic>Advances in Applied Probability<\/jats:italic>17, 841\u2013867) and Bai, Lumsdaine, and Stock (1998,<jats:italic>Review of Economic Studies<\/jats:italic>65, 395\u2013432), where the magnitude of changed parameters depends on the sample size<jats:italic>n<\/jats:italic>and tends to zero as<jats:italic>n<\/jats:italic>\u2192 \u221e. The theory is applied for the self-weighted QMLE and the local QMLE of change-points in ARMA-GARCH\/IGARCH models. A simulation study is carried out to evaluate the performance of these estimators in the finite sample.<\/jats:p>","DOI":"10.1017\/s0266466614000863","type":"journal-article","created":{"date-parts":[[2014,12,4]],"date-time":"2014-12-04T10:21:30Z","timestamp":1417688490000},"page":"402-430","source":"Crossref","is-referenced-by-count":21,"title":["ESTIMATION OF CHANGE-POINTS IN LINEAR AND NONLINEAR TIME SERIES MODELS"],"prefix":"10.1017","volume":"32","author":[{"given":"Shiqing","family":"Ling","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,12,4]]},"reference":[{"key":"S0266466614000863_ref2","doi-asserted-by":"publisher","DOI":"10.2307\/2951753"},{"key":"S0266466614000863_ref37","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2006.00754.x"},{"key":"S0266466614000863_ref14","doi-asserted-by":"publisher","DOI":"10.1198\/016214505000000745"},{"key":"S0266466614000863_ref16","doi-asserted-by":"publisher","DOI":"10.3150\/bj\/1093265632"},{"key":"S0266466614000863_ref31","doi-asserted-by":"publisher","DOI":"10.1214\/009053606000001514"},{"key":"S0266466614000863_ref32","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2006.07.016"},{"key":"S0266466614000863_ref7","doi-asserted-by":"publisher","DOI":"10.2307\/2998540"},{"key":"S0266466614000863_ref3","doi-asserted-by":"publisher","DOI":"10.1214\/09-AOS707"},{"key":"S0266466614000863_ref19","first-page":"321","article-title":"Tests for parameters instability in regression with I(1) processes","volume":"10","author":"Hansen","year":"1992","journal-title":"Journal of Business and Economic Statistics"},{"key":"S0266466614000863_ref20","doi-asserted-by":"publisher","DOI":"10.1257\/jep.15.4.117"},{"key":"S0266466614000863_ref15","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176348257"},{"key":"S0266466614000863_ref34","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9574.2009.00447.x"},{"key":"S0266466614000863_ref10","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466601171045"},{"key":"S0266466614000863_ref38","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1960.10482067"},{"key":"S0266466614000863_ref8","volume-title":"Convergence of Probability Measures","author":"Billingsley","year":"1968"},{"key":"S0266466614000863_ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2008.07.001"},{"key":"S0266466614000863_ref35","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466613000388"},{"key":"S0266466614000863_ref43","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466609990788"},{"key":"S0266466614000863_ref12","volume-title":"Probability Theory. 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