, Volume 28, Issue 2, pp 499–521 | Cite as

A new class of tests for multinormality with i.i.d. and garch data based on the empirical moment generating function

  • Norbert Henze
  • María Dolores Jiménez-GameroEmail author
Original Paper


We generalize a recent class of tests for univariate normality that are based on the empirical moment generating function to the multivariate setting, thus obtaining a class of affine invariant, consistent and easy-to-use goodness-of-fit tests for multinormality. The test statistics are suitably weighted \(L^2\)-statistics, and we provide their asymptotic behavior both for i.i.d. observations and in the context of testing that the innovation distribution of a multivariate GARCH model is Gaussian. We study the finite-sample behavior of the new tests, compare the criteria with alternative existing procedures, and apply the new procedure to a data set of monthly log returns.


Moment generating function Goodness-of-fit test Multivariate normality Gaussian GARCH model 

Mathematics Subject Classification

62H15 62G20 



M.D. Jiménez-Gamero was partially supported by Grants MTM2014-55966-P, of the Spanish Ministry of Economy and Competitiveness, and MTM2017-89422-P, of the Spanish Ministry of Economy, Industry and Competitiveness, ERDF support included.


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Copyright information

© Sociedad de Estadística e Investigación Operativa 2018

Authors and Affiliations

  • Norbert Henze
    • 1
  • María Dolores Jiménez-Gamero
    • 2
    Email author
  1. 1.Institute of StochasticsKarlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.Department of Statistics and Operations ResearchUniversity of SevilleSevilleSpain

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