Title: 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.