| Institution: | 1.Department of Economics,University of Copenhagen,Copenhagen K,Denmark;2.Department of Mathematical Sciences,University of Copenhagen,Copenhagen ?,Denmark;3.Université Pierre et Marie Curie, LSTA,Paris,France |
| 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 (VSRV), closely related to non-standard regular variation. The characterization of the tail behavior of the processes is used for deriving the asymptotic properties of the sample covariance matrices. |
