Characterization of the tail behavior of a class of BEKK processes: A stochastic recurrence equation approach

We provide new, mild conditions for strict stationarity and ergodicity of a class of BEKK processes. By exploiting that the processes can be represented as multivariate stochastic recurrence equations, we characterize the tail behavior of the associated stationary laws. Specifically, we show that the each component of the BEKK processes is regularly varying with some tail index. In general, the tail index differs along the components, which contrasts most of the existing literature on the tail behavior of multivariate GARCH processes.