  In this paper we obtain new limit theorems for variational functionals of
high frequency observations of stationary increments L\'evy driven moving
averages. We will see that the asymptotic behaviour of such functionals heavily
depends on the kernel, the driving L\'evy process and the properties of the
functional under consideration. We show the "law of large numbers" for our
class of statistics, which consists of three different cases. For one of the
appearing limits, which we refer to as the ergodic type limit, we also prove
the associated weak limit theory, which again consists of three different
cases. Our work is related to [9,10], who considered power variation
functionals of stationary increments L\'evy driven moving averages.
