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We define convergence in terms of a decrease in dispersion over time and model this decrease via mechanisms that allow for gradual reductions in the ranks of covariance matrices associated with the disturbance vectors driving the unobserved components of the model. The inclusion of such convergence mechanisms within the formulation of unobserved components makes the identification of various types of convergence possible. The common converging component model is estimated for the per capita gross domestic product of five European countries: Germany, France, Italy, Spain and the Netherlands. It is found that convergence features in trends and cycles are present and are associated with some key events in the history of European integration. Copyright \u00a9 2004 John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/jae.785","type":"journal-article","created":{"date-parts":[[2004,9,28]],"date-time":"2004-09-28T12:00:22Z","timestamp":1096372822000},"page":"611-636","source":"Crossref","is-referenced-by-count":32,"title":["Convergence in European GDP series: a multivariate common converging trend\u2013cycle decomposition"],"prefix":"10.1002","volume":"19","author":[{"given":"Rob","family":"Luginbuhl","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Siem Jan","family":"Koopman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2004,9,28]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1086\/261816"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/jae.3950100202"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(94)01699-2"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3932(81)90040-4"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.1162\/003465302317331964"},{"key":"e_1_2_8_7_1","volume-title":"Object\u2010Oriented Matrix Programming using Ox","author":"Doornik JA","year":"1999"},{"key":"e_1_2_8_8_1","unstructured":"DoornikJA HansenH.1994.An omnibus test of univariate and multivariate normality. 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