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

Published online by Cambridge University Press:  22 May 2018

Norbert Henze ,
M. Dolores Jiménez–Gamero  and
Simos G. Meintanis
Norbert Henze
Affiliation:
Institute of Stochastics, Karlsruhe Institute of Technology
M. Dolores Jiménez–Gamero
Affiliation:
University of Seville
Simos G. Meintanis*
Affiliation:
National and Kapodistrian University of Athens and North–West University
*
*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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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.

Type
ARTICLES
Information
Econometric Theory , Volume 35 , Issue 3 , June 2019 , pp. 510 - 546
Copyright
Copyright © Cambridge University Press 2018 

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Footnotes

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.

References

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