Dependence Estimation for High Frequency Sampled Multivariate CARMA Models

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 crosscovariances between different components of the model. We will see that the limit distribution of the sample autocovariance function has the same structure in the continuous-time and in the discrete-time model. However, there is a difference in the fourth moment part. A special case is the CARMA (the one-dimensional MCARMA) process. For a CARMA process we prove Bartlett's formula for the sample correlation function; in contrast Bartlett's formula is the same in both models. Finally, we present limit results for multivariate MA processes as well which are not known in this generality in the multivariate setting yet.