In this paper we consider a continuous-time autoregressive moving average (CARMA) process (Yt)t∈R driven by a symmetric α-stable Lévy process with α∈(0,2] sampled at a high-frequency time-grid {0,Δn,2Δn,…,nΔn}, where the observation grid gets finer and the last observation tends to...

Conditions for the existence of strictly stationary multivariate GARCH processes in the so-called BEKK parametrisation, which is the most general form of multivariate GARCH processes typically used in applications, and for their geometric ergodicity are obtained. The conditions are that the...