  Interest in continuous-time processes has increased rapidly in recent years,
largely because of high-frequency data available in many applications. We
develop a method for estimating the kernel function $g$ of a second-order
stationary L\'evy-driven continuous-time moving average (CMA) process $Y$ based
on observations of the discrete-time process $Y^\Delta$ obtained by sampling
$Y$ at $\Delta, 2\Delta,...,n\Delta$ for small $\Delta$. We approximate $g$ by
$g^\Delta$ based on the Wold representation and prove its pointwise convergence
to $g$ as $\Delta\rightarrow 0$ for $\CARMA(p,q)$ processes. Two non-parametric
estimators of $g^\Delta$, based on the innovations algorithm and the
Durbin-Levinson algorithm, are proposed to estimate $g$. For a Gaussian CARMA
process we give conditions on the sample size $n$ and the grid-spacing
$\Delta(n)$ under which the innovations estimator is consistent and
asymptotically normal as $n\rightarrow\infty$. The estimators can be calculated
from sampled observations of {\it any} CMA process and simulations suggest that
they perform well even outside the class of CARMA processes. We illustrate
their performance for simulated data and apply them to the Brookhaven turbulent
wind speed data. Finally we extend results of \citet{bfk:2011:1} for sampled
CARMA processes to a much wider class of CMA processes.
