{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T05:34:10Z","timestamp":1776749650266,"version":"3.51.2"},"reference-count":21,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2010,10,18]],"date-time":"2010-10-18T00:00:00Z","timestamp":1287360000000},"content-version":"unspecified","delay-in-days":7626,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1989,12]]},"abstract":"<jats:p>For a first-order autoregressive process <jats:italic>Y<jats:sub>t<\/jats:sub><\/jats:italic> = \u03b2<jats:italic>Y<\/jats:italic><jats:sub>t\u22121<\/jats:sub> + <jats:italic>\u2208<jats:sub>t<\/jats:sub><\/jats:italic> where the \u2208<jats:italic><jats:sub>t<\/jats:sub><\/jats:italic>'S are i.i.d. and belong to the domain of attraction of a stable law, the strong consistency of the ordinary least-squares estimator <jats:italic>b<jats:sub>n<\/jats:sub><\/jats:italic> of <jats:italic>\u03b2<\/jats:italic> is obtained for <jats:italic>\u03b2<\/jats:italic> = 1, and the limiting distribution of <jats:italic>b<jats:sub>n<\/jats:sub><\/jats:italic> is established as a functional of a L\u00e9vy process. Generalizations to seasonal difference models are also considered. These results are useful in testing for the presence of unit roots when the \u2208<jats:italic><jats:sub>t<\/jats:sub><\/jats:italic>'S are heavy-tailed.<\/jats:p>","DOI":"10.1017\/s0266466600012561","type":"journal-article","created":{"date-parts":[[2010,10,18]],"date-time":"2010-10-18T09:15:33Z","timestamp":1287393333000},"page":"354-362","source":"Crossref","is-referenced-by-count":96,"title":["On the First-Order Autoregressive Process with Infinite Variance"],"prefix":"10.1017","volume":"5","author":[{"given":"Ngai Hang","family":"Chan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lanh Tat","family":"Tran","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2010,10,18]]},"reference":[{"key":"S0266466600012561_ref008","volume-title":"Introduction to statistical time series","author":"Fuller","year":"1976"},{"key":"S0266466600012561_ref016","doi-asserted-by":"publisher","DOI":"10.1086\/296024"},{"key":"S0266466600012561_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0064907"},{"key":"S0266466600012561_ref018","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177692473"},{"key":"S0266466600012561_ref011","doi-asserted-by":"publisher","DOI":"10.1007\/BF00575529"},{"key":"S0266466600012561_ref002","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177697609"},{"key":"S0266466600012561_ref001","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176350492"},{"key":"S0266466600012561_ref005","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176346318"},{"key":"S0266466600012561_ref003","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176349937"},{"key":"S0266466600012561_ref017","doi-asserted-by":"publisher","DOI":"10.1007\/BF00538475"},{"key":"S0266466600012561_ref006","doi-asserted-by":"publisher","DOI":"10.1086\/294743"},{"key":"S0266466600012561_ref014","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176345697"},{"key":"S0266466600012561_ref019","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/74.3.535"},{"key":"S0266466600012561_ref020","unstructured":"20. Phillips P.C.B. Personal communication (1988)."},{"key":"S0266466600012561_ref004","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1984.10478057"},{"key":"S0266466600012561_ref007","volume-title":"An introduction to probability theory and its applications","volume":"2","author":"Feller","year":"1976"},{"key":"S0266466600012561_ref009","doi-asserted-by":"publisher","DOI":"10.2307\/3213015"},{"key":"S0266466600012561_ref015","doi-asserted-by":"publisher","DOI":"10.2307\/2525574"},{"key":"S0266466600012561_ref012","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.1987.tb00420.x"},{"key":"S0266466600012561_ref013","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511897221"},{"key":"S0266466600012561_ref021","doi-asserted-by":"publisher","DOI":"10.2307\/1427239"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466600012561","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,19]],"date-time":"2019-05-19T19:04:44Z","timestamp":1558292684000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466600012561\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,12]]},"references-count":21,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1989,12]]}},"alternative-id":["S0266466600012561"],"URL":"https:\/\/doi.org\/10.1017\/s0266466600012561","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,12]]}}}