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We consider high-frequency sampled continuous-time autoregressive movingaverage (CARMA) models driven by finite-variance zero-mean L\'evy processes. AnL^2-consistent estimator for the increments of the driving L\'evy processwithout order selection in advance is proposed if the CARMA model isinvertible. In the second part we analyse the high-frequency behaviour ofapproximating Riemann sum processes, which represent a natural way to simulatecontinuous-time moving average processes on a discrete grid. We shall comparetheir autocovariance structure with the one of sampled CARMA processes, wherethe rule of integration plays a crucial role. Moreover, new insight into thekernel estimation procedure of Brockwell et al. (2012a) is given.

Noise recovery for L\'evy-driven CARMA processes and high-frequency behaviour of approximating Riemann sums