  The class of multivariate L\'{e}vy-driven autoregressive moving average
(MCARMA) processes, the continuous-time analogs of the classical vector ARMA
processes, is shown to be equivalent to the class of continuous-time state
space models. The linear innovations of the weak ARMA process arising from
sampling an MCARMA process at an equidistant grid are proved to be
exponentially completely regular ($\beta$-mixing) under a mild continuity
assumption on the driving L\'{e}vy process. It is verified that this continuity
assumption is satisfied in most practically relevant situations, including the
case where the driving L\'{e}vy process has a non-singular Gaussian component,
is compound Poisson with an absolutely continuous jump size distribution or has
an infinite L\'{e}vy measure admitting a density around zero.
