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Tests for conditional ellipticity in multivariate GARCH models

Christian Francq (), Jiménez-Gamero, M.D. and S.G. Meintanis

Journal of Econometrics, 2017, vol. 196, issue 2, 305-319

Abstract: Tests are proposed for the assumption that the conditional distribution of a multivariate GARCH process is elliptic. These tests are of Kolmogorov–Smirnov and Cramér–von Mises-type and make use of the common geometry underlying the characteristic function of any spherically symmetric distribution. The asymptotic null distribution of the test statistics as well as the consistency of the tests is investigated under general conditions. It is shown that both the finite sample and the asymptotic null distribution depend on the unknown distribution of the Euclidean norm of the innovations. Therefore a conditional Monte Carlo procedure is used to actually carry out the tests. The validity of this resampling scheme is formally justified. Results on the behavior of the new tests in finite-samples are included along with comparisons with other tests.

Keywords: MGARCH; Spherical symmetry; Empirical characteristic function; Conditional Monte Carlo test; Extended CCC-GARCH (search for similar items in EconPapers)
JEL-codes: C12 C15 C32 C58 (search for similar items in EconPapers)
Date: 2017
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