Extreme value theory for moving average processes with light-tailed innovations

We consider stationary infinite moving average processes of the
form $Y_n = \sum c_i Z_{n+i}$, where the sum ranges over the
integers, (Z_i) is a sequence of iid random variables with ``light
tails'' and (c_i) is a sequence of positive and summable
coefficients. By light tails we mean that Z_0 has a bounded density
$f(t)$ behaving asymptotically like $v(t) \exp (-g(t) )$, where
v(t) behaves roughly like a constant as t goes to infinity, and
g(t) is strictly convex satisfying certain asymptotic regularity
conditions. We show that the iid sequence associated with Y_0 is in
the maximum domain of attraction of the Gumbel distribution. Under
additional regular variation conditions on g, it is shown that the
stationary sequence (Y_n) has the same extremal behaviour as its
associated iid sequence. This generalizes results of Rootz\'en
(1986, 1987), where $g(t) = t^p$ and $v(t)=c t^d$ for p > 1,
positive c and a real constant d.