Conditions for geometric ergodicity of multivariate ARCH processes, with the so-called BEKK  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  ). The characterization of the tail behavior of the processes is used for deriving the asymptotic distribution of the sample covariance matrices.
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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ARCH
autoregressive conditional heteroskedasticity (ARCH)
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(Baba, Engle, Kraft, and Kroner)
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, Advances in Applied Probability, 29, pp. 138-164
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distribution
properties