{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T05:34:09Z","timestamp":1776749649779,"version":"3.51.2"},"reference-count":29,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2009,2,11]],"date-time":"2009-02-11T00:00:00Z","timestamp":1234310400000},"content-version":"unspecified","delay-in-days":4393,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1997,2]]},"abstract":"<jats:p>This paper generalizes the univariate results of Chan and Tran (1989, <jats:italic>Econometric Theory<\/jats:italic> 5, 354\u2013362) and Phillips (1990, <jats:italic>Econometric Theory<\/jats:italic> 6, 44\u201362) to multivariate time series. We develop the limit theory for the least-squares estimate of a VAR(l) for a random walk with independent and identically distributed errors and for I(1) processes with weakly dependent errors whose distributions are in the domain of attraction of a stable law. The limit laws are represented by functional of a stable process. A semiparametric correction is used in order to asymptotically eliminate the \u201cbias\u201d term in the limit law. These results are also an extension of the multivariate limit theory for square-integrable disturbances derived by Phillips and Durlauf (1986, <jats:italic>Review of Economic Studies<\/jats:italic> 53, 473\u2013495). Potential applications include tests for multivariate unit roots and cointegration.<\/jats:p>","DOI":"10.1017\/s0266466600005983","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T15:35:15Z","timestamp":1236699315000},"page":"506-528","source":"Crossref","is-referenced-by-count":15,"title":["Weak Convergence to a Matrix Stochastic Integral with Stable Processes"],"prefix":"10.1017","volume":"13","author":[{"given":"Mehmet","family":"Caner","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S0266466600005983_ref015","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600007982"},{"key":"S0266466600005983_ref010","doi-asserted-by":"publisher","DOI":"10.1086\/294743"},{"key":"S0266466600005983_ref013","unstructured":"Jeganathan P. (1996) On Asymptotic Inference in Linear Cointegrated Time Series Systems. 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