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

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  • Norbert Henze

    (Karlsruhe Institute of Technology)

  • María Dolores Jiménez-Gamero

    (University of Seville)

Abstract

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 $$L^2$$ 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.

Suggested Citation

  • Norbert Henze & María Dolores Jiménez-Gamero, 2019. "A new class of tests for multinormality with i.i.d. and garch data based on the empirical moment generating function," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 499-521, June.
    • Handle: RePEc:spr:testjl:v:28:y:2019:i:2:d:10.1007_s11749-018-0589-z
    DOI: 10.1007/s11749-018-0589-z
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    Cited by:

    1. M. Dolores Jiménez-Gamero, 2020. "Comments on: Tests for multivariate normality—a critical review with emphasis on weighted $$L^2$$ L 2 -statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 893-897, December.
    2. Norbert Henze & María Dolores Jiménez‐Gamero, 2021. "A test for Gaussianity in Hilbert spaces via the empirical characteristic functional," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 406-428, June.
    3. Bruno Ebner & Norbert Henze, 2020. "Tests for multivariate normality—a critical review with emphasis on weighted $$L^2$$ L 2 -statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 845-892, December.
    4. Steffen Betsch & Bruno Ebner, 2021. "Fixed point characterizations of continuous univariate probability distributions and their applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 31-59, February.
    5. Philip Dörr & Bruno Ebner & Norbert Henze, 2021. "A new test of multivariate normality by a double estimation in a characterizing PDE," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(3), pages 401-427, April.

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