  Consider a moving average process $X$ of the form $X(t)=\int_{-\infty}^t
x(t-u)dZ_u$, $t\geq 0$, where $Z$ is a (non Gaussian) Hermite process of order
$q\geq 2$ and $x:\mathbb{R}_+\to\mathbb{R}$ is sufficiently integrable. This
paper investigates the fluctuations, as $T\to\infty$, of integral functionals
of the form $t\mapsto \int_0^{Tt }P(X(s))ds$, in the case where $P$ is any
given polynomial function. It extends a study initiated in Tran (2018), where
only the quadratic case $P(x)=x^2$ and the convergence in the sense of
finite-dimensional distributions were considered.
