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We consider a L\'evy driven continuous time moving average process $X$sampled at random times which follow a renewal structure independent of $X$.Asymptotic normality of the sample mean, the sample autocovariance, and thesample autocorrelation is established under certain conditions on the kerneland the random times. We compare our results to a classical non-randomequidistant sampling method and give an application to parameter estimation ofthe L\'evy driven Ornstein-Uhlenbeck process.

On the sample autocovariance of a L\'evy driven moving average process when sampled at a renewal sequence