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High-frequency sampled multivariate continuous time autoregressive movingaverage processes are investigated. We obtain asymptotic expansion for thespectral density of the sampled MCARMA process $(Y_{n\Delta})_{n \in\mathbb{Z}}$ as $\Delta \downarrow 0$, where $(Y_t)_{t \in \mathbb{R}}$ is anMCARMA process. We show that the properly filtered process is a vector movingaverage process, and determine the asymptotic moving average representation ofit, thus generalizing the results by Brockwell et al. in the univariate case tothe multivariate model. The determination of the moving average representationof the filtered process, important for the analysis of high-frequency data, isdifficult for any fixed positive $\Delta$. However, the results establishedhere provide a useful and insightful approximation when $\Delta$ is very small.

High-frequency sampling of multivariate CARMA processes