{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,24]],"date-time":"2026-10-24T02:26:14Z","timestamp":1792808774618,"version":"4.5.0"},"reference-count":31,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2009,4,1]],"date-time":"2009-04-01T00:00:00Z","timestamp":1238544000000},"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":[[2009,4]]},"abstract":"<jats:p>An asymptotic theory is developed for multivariate regression in cointegrated systems whose variables are moderately integrated or moderately explosive in the sense that they have autoregressive roots of the form <jats:italic>\u03c1<jats:sub>ni<\/jats:sub><\/jats:italic> = 1 + <jats:italic>c<jats:sub>i<\/jats:sub><\/jats:italic>\/<jats:italic>n<jats:sup>\u03b1<\/jats:sup><\/jats:italic>, involving moderate deviations from unity when <jats:italic>\u03b1<\/jats:italic> \u2208 (0, 1) and <jats:italic>c<jats:sub>i<\/jats:sub><\/jats:italic> \u2208 \u211d are constant parameters. When the data are moderately integrated in the stationary direction (with <jats:italic>c<jats:sub>i<\/jats:sub><\/jats:italic> &lt; 0), it is shown that least squares regression is consistent and asymptotically normal but suffers from significant bias, related to simultaneous equations bias. In the moderately explosive case (where <jats:italic>c<jats:sub>i<\/jats:sub><\/jats:italic> &gt; 0) the limit theory is mixed normal with Cauchy-type tail behavior, and the rate of convergence is explosive, as in the case of a moderately explosive scalar autoregression (Phillips and Magdalinos, 2007, <jats:italic>Journal of Econometrics<\/jats:italic> 136, 115\u2013130). Moreover, the limit theory applies without any distributional assumptions and for weakly dependent errors under conventional moment conditions, so an invariance principle holds, unlike the well-known case of an explosive autoregression. This theory validates inference in cointegrating regression with mildly explosive regressors. The special case in which the regressors themselves have a common explosive component is also considered.<\/jats:p>","DOI":"10.1017\/s0266466608090154","type":"journal-article","created":{"date-parts":[[2009,1,30]],"date-time":"2009-01-30T09:47:27Z","timestamp":1233308847000},"page":"482-526","source":"Crossref","is-referenced-by-count":84,"title":["LIMIT THEORY FOR COINTEGRATED SYSTEMS WITH MODERATELY INTEGRATED AND MODERATELY EXPLOSIVE REGRESSORS"],"prefix":"10.1017","volume":"25","author":[{"given":"Tassos","family":"Magdalinos","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter C.B.","family":"Phillips","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2009,4,1]]},"reference":[{"key":"S0266466608090154_ref22","doi-asserted-by":"publisher","DOI":"10.2307\/2297602"},{"key":"S0266466608090154_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/0165-1889(88)90041-3"},{"key":"S0266466608090154_ref19","doi-asserted-by":"publisher","DOI":"10.2307\/2951476"},{"key":"S0266466608090154_ref1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511810800"},{"key":"S0266466608090154_ref21","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2006.05.017"},{"key":"S0266466608090154_ref14","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/74.3.535"},{"key":"S0266466608090154_ref10","doi-asserted-by":"publisher","DOI":"10.1017\/S026646660000997X"},{"key":"S0266466608090154_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(97)00004-3"},{"key":"S0266466608090154_ref4","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176350492"},{"key":"S0266466608090154_ref15","doi-asserted-by":"publisher","DOI":"10.2307\/1911357"},{"key":"S0266466608090154_ref18","doi-asserted-by":"publisher","DOI":"10.2307\/2938169"},{"key":"S0266466608090154_ref31","doi-asserted-by":"publisher","DOI":"10.2307\/2951763"},{"key":"S0266466608090154_ref25","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2005.08.002"},{"key":"S0266466608090154_ref30","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600004217"},{"key":"S0266466608090154_ref26","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511493157.008"},{"key":"S0266466608090154_ref2","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177706198"},{"key":"S0266466608090154_ref28","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466608080353"},{"key":"S0266466608090154_ref5","doi-asserted-by":"publisher","DOI":"10.2307\/2998544"},{"key":"S0266466608090154_ref6","volume-title":"Martingale Limit Theory and Its Application","author":"Hall","year":"1980"},{"key":"S0266466608090154_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02514-7"},{"key":"S0266466608090154_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(94)01664-L"},{"key":"S0266466608090154_ref12","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600013402"},{"key":"S0266466608090154_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/0047-259X(85)90056-9"},{"key":"S0266466608090154_ref16","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/080\/999009"},{"key":"S0266466608090154_ref17","doi-asserted-by":"publisher","DOI":"10.2307\/2938258"},{"key":"S0266466608090154_ref20","doi-asserted-by":"publisher","DOI":"10.2307\/2171721"},{"key":"S0266466608090154_ref23","doi-asserted-by":"publisher","DOI":"10.2307\/2297545"},{"key":"S0266466608090154_ref24","doi-asserted-by":"publisher","DOI":"10.2307\/2298004"},{"key":"S0266466608090154_ref27","volume-title":"Inference in Cointegrated Systems with Mildly Integrated Regressors","author":"Phillips","year":"2008"},{"key":"S0266466608090154_ref29","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176348666"},{"key":"S0266466608090154_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600010434"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466608090154","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,8]],"date-time":"2019-04-08T20:31:10Z","timestamp":1554755470000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466608090154\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,4]]},"references-count":31,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2009,4]]}},"alternative-id":["S0266466608090154"],"URL":"https:\/\/doi.org\/10.1017\/s0266466608090154","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,4]]}}}