Multivariate COGARCH(1,1) Processes

Multivariate COGARCH(1, 1) processes are introduced as a continuous-time models for multidimensional heteroskedastic observations. Our model is driven by a single multivariate Lévy process and the latent timevarying covariance matrix is directly specified as a stochastic process in the positive semidefinite matrices. After defining the COGARCH(1, 1) process, we analyze its probabilistic properties.We show a sufficient condition for the existence of a stationary distribution for the stochastic covariance matrix process and present criteria ensuring the finiteness of moments. Under certain natural assumptions on themoments of the driving Lévy process, explicit expressions for the first and second-order moments and (asymptotic) secondorder stationarity of the covariance matrix process are obtained. Furthermore, we study the stationarity and second-order structure of the increments of the multivariate COGARCH(1, 1) process and their “squares”.     «

Multivariate COGARCH(1, 1) processes are introduced as a continuous-time models for multidimensional heteroskedastic observations. Our model is driven by a single multivariate Lévy process and the latent timevarying covariance matrix is directly specified as a stochastic process in the positive semidefinite matrices. After defining the COGARCH(1, 1) process, we analyze its probabilistic properties.We show a sufficient condition for the existence of a stationary distribution for the stochasti...     »