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

Norbert Henze and María Dolores Jiménez-Gamero ()
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Norbert Henze: Karlsruhe Institute of Technology
María Dolores Jiménez-Gamero: University of Seville

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2019, vol. 28, issue 2, No 17, 499-521

Abstract: 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.

Keywords: Moment generating function; Goodness-of-fit test; Multivariate normality; Gaussian GARCH model; 62H15; 62G20 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s11749-018-0589-z

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