On the tail behavior of a class of multivariate conditionally heteroskedastic processes

Abstract : Conditions for geometric ergodicity of multivariate autoregressive conditional heteroskedasticity (ARCH) processes, with the so-called BEKK (Baba, Engle, Kraft, and Kroner) parametrization, are considered. We show for a class of BEKK-ARCH processes that the invariant distribution is regularly varying. In order to account for the possibility of different tail indices of the marginals, we consider the notion of vector scaling regular variation, in the spirit of Perfekt (1997, Advances in Applied Probability, 29, pp. 138-164). The characterization of the tail behavior of the processes is used for deriving the asymptotic properties of the sample covariance matrices.
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Extremes, Springer Verlag (Germany), In press
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Contributeur : Olivier Wintenberger <>
Soumis le : vendredi 1 décembre 2017 - 16:42:53
Dernière modification le : jeudi 13 décembre 2018 - 01:30:05

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  • HAL Id : hal-01436267, version 3
  • ARXIV : 1701.05091

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Rasmus Pedersen, Olivier Wintenberger. On the tail behavior of a class of multivariate conditionally heteroskedastic processes. Extremes, Springer Verlag (Germany), In press. 〈hal-01436267v3〉

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