  The paper considers high frequency sampled multivariate continuous-time ARMA
(MCARMA) models, and derives the asymptotic behavior of the sample
autocovariance function to a normal random matrix. Moreover, we obtain the
asymptotic behavior of the cross-covariances between different components of
the model. We will see that the limit distribution of the sample autocovariance
function has a similar structure in the continuous-time and in the
discrete-time model. As special case we consider a CARMA (one-dimensional
MCARMA) process. For a CARMA process we prove Bartlett's formula for the sample
autocorrelation function. Bartlett's formula has the same form in both models,
only the sums in the discrete-time model are exchanged by integrals in the
continuous-time model. Finally, we present limit results for multivariate MA
processes as well which are not known in this generality in the multivariate
setting yet.
