{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T13:50:59Z","timestamp":1790689859934,"version":"4.1.0"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2000,12,15]],"date-time":"2000-12-15T00:00:00Z","timestamp":976838400000},"content-version":"unspecified","delay-in-days":14,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2000,12]]},"abstract":"<jats:p>This paper develops a new estimation method for \nnonstationary vector autoregressions (VAR's) with \nunknown mixtures of <jats:italic>I<\/jats:italic>(0), <jats:italic>I<\/jats:italic>(1), and \n<jats:italic>I<\/jats:italic>(2) components. The method does not require \nprior knowledge on the exact number and location of unit \nroots in the system. It is, therefore, applicable for \nVAR's with any mixture of <jats:italic>I<\/jats:italic>(0), <jats:italic>I<\/jats:italic>(1), \nand <jats:italic>I<\/jats:italic>(2) variables, which may be cointegrated in \nany form. The limit theory for the stationary component of \nour estimator is still normal, thereby preserving the usual \nVAR limit theory. Yet, the leading term of the nonstationary \ncomponent of the estimator has mixed normal limit distribution \nand does not involve unit root distribution. Our method is an \nextension of the FM-VAR procedure by Phillips (1995, \n<jats:italic>Econometrica<\/jats:italic> 63, 1023\u20131078) and yields an estimator \nthat is optimal in the sense of Phillips (1991, <jats:italic>Econometrica<\/jats:italic> \n59, 283\u2013306). Moreover, we show for a certain class of \nlinear restrictions that the Wald tests based on the estimator \nare asymptotically distributed as a weighted sum of independent \nchi-square variates with weights between zero and one. For \nsuch restrictions, the limit distribution of the standard Wald \ntest is nonstandard and nuisance parameter dependent. This has \na direct application for Granger-causality testing in nonstationary \nVAR's.<\/jats:p>","DOI":"10.1017\/s0266466600166058","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T09:45:46Z","timestamp":1027763146000},"page":"905-926","source":"Crossref","is-referenced-by-count":4,"title":["VECTOR AUTOREGRESSIONS WITH UNKNOWN MIXTURES OF <i>I<\/i>(0), \n<i>I<\/i>(1), AND <i>I<\/i>(2) COMPONENTS"],"prefix":"10.1017","volume":"16","author":[{"given":"Yoosoon","family":"Chang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2000,12,15]]},"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466600166058","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,8]],"date-time":"2019-05-08T15:44:46Z","timestamp":1557330286000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466600166058\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,12]]},"references-count":0,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2000,12]]}},"alternative-id":["S0266466600166058"],"URL":"https:\/\/doi.org\/10.1017\/s0266466600166058","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,12]]}}}