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CHARACTERIZATIONS OF MULTINORMALITY AND CORRESPONDING TESTS OF FIT, INCLUDING FOR GARCH MODELS

  • Norbert Henze (a1), M. Dolores Jiménez–Gamero (a2) and Simos G. Meintanis (a3)
Abstract

We provide novel characterizations of multivariate normality that incorporate both the characteristic function and the moment generating function, and we employ these results to construct a class of affine invariant, consistent and easy-to-use goodness-of-fit tests for normality. The test statistics are suitably weighted L2-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.

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Corresponding author
*Address correspondence to Simos G. Meintanis, Department of Economics, National and Kapodistrian University of Athens, Athens, Greece; e-mail: simosmei@econ.uoa.gr and Unit for Business Mathematics and Informatics, North–West University, Potchefstroom, South Africa.
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The authors thank the anonymous reviewers for their constructive comments. M.D. Jiménez-Gamero was partially supported by MTM2017–89422–P of the Spanish Ministry of Economy, Industry and Competitiveness/ERDF. Simos Meintanis was partially supported by grant Nr. 11699 of the Special Account for Research Grants (EΛKE) of the National and Kapodistrian University of Athens.

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Econometric Theory
  • ISSN: 0266-4666
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