On the sample autocovariance of a Lévy driven moving average process when sampled at a renewal sequence

We consider a L\évy 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 the sample autocorrelation is established under certain conditions on the kernel and the random times. We compare our results to a classical non-random equidistant sampling method and give an application to parameter estimation of the L\évy driven Ornstein-Uhlenbeck process.