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

Rasmus Pedersen () and Olivier Wintenberger ()
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Rasmus Pedersen: Department of Economics - University of Copenhagen - KU - University of Copenhagen = Københavns Universitet
Olivier Wintenberger: LSTA - Laboratoire de Statistique Théorique et Appliquée - UPMC - Université Pierre et Marie Curie - Paris 6 - CNRS - Centre National de la Recherche Scientifique, University of Copenhagen - Department of Mathematical Sciences - KU - University of Copenhagen = Københavns Universitet

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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.

Keywords: geometric ergodicity; asymptotic properties; Stochastic recurrence equations; Markov processes; regular variation; multivariate ARCH (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ets
Date: 2017
Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-01436267v3
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Published in Extremes, Springer Verlag (Germany), In press

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