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

• Norbert Henze ^[1] ; María Dolores Jiménez-Gamero ^[2]
  1. [1] Karlsruhe Institute of Technology

     Karlsruhe Institute of Technology

     Stadtkreis Karlsruhe, Alemania

     
  2. [2] Universidad de Sevilla

     Universidad de Sevilla

     Sevilla, España

     
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 28, Nº. 2, 2019, págs. 499-521
• Idioma: inglés
• DOI: 10.1007/s11749-018-0589-z
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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 L2 -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