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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Date: June 2019
From: Test(Vol. 28, Issue 2)
Publisher: Springer
Document Type: Report
Length: 173 words

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Byline: Norbert Henze (1), Maria Dolores Jimenez-Gamero (2) Keywords: Moment generating function; Goodness-of-fit test; Multivariate normality; Gaussian GARCH model; 62H15; 62G20 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.sup.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. Author Affiliation: (1) 0000 0001 0075 5874, grid.7892.4, Institute of Stochastics, Karlsruhe Institute of Technology, Karlsruhe, Germany (2) 0000 0001 2168 1229, grid.9224.d, Department of Statistics and Operations Research, University of Seville, Seville, Spain Article History: Registration Date: 22/05/2018 Received Date: 19/11/2017 Accepted Date: 11/05/2018 Online Date: 30/05/2018

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Gale Document Number: GALE|A588849241