  In this article we consider L\'evy driven continuous time moving average
processes observed on a lattice, which are stationary time series. We show
asymptotic normality of the sample mean, the sample autocovariances and the
sample autocorrelations. A comparison with the classical setting of discrete
moving average time series shows that in the last case a correction term should
be added to the classical Bartlett formula that yields the asymptotic variance.
An application to the asymptotic normality of the estimator of the Hurst
exponent of fractional L\'evy processes is also deduced from these results.
