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The test statistics are suitably weighted<jats:italic>L<\/jats:italic><jats:sup>2<\/jats:sup>-statistics, and we provide their asymptotic behavior both for i.i.d. observations as well as in the context of testing that the innovation distribution of a multivariate GARCH model is Gaussian. We also study the finite-sample behavior of the new tests and compare the new criteria with alternative existing tests.<\/jats:p>","DOI":"10.1017\/s0266466618000154","type":"journal-article","created":{"date-parts":[[2018,5,22]],"date-time":"2018-05-22T09:27:05Z","timestamp":1526981225000},"page":"510-546","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":22,"title":["CHARACTERIZATIONS OF MULTINORMALITY AND CORRESPONDING TESTS OF FIT, INCLUDING FOR GARCH MODELS"],"prefix":"10.1017","volume":"35","author":[{"given":"Norbert","family":"Henze","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M. 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