  We consider sequences of random variables of the type $S_n= n^{-1/2}
\sum_{k=1}^n \{f(X_k)-\E[f(X_k)]\}$, $n\geq 1$, where $X=(X_k)_{k\in \Z}$ is a
$d$-dimensional Gaussian process and $f: \R^d \rightarrow \R$ is a measurable
function. It is known that, under certain conditions on $f$ and the covariance
function $r$ of $X$, $S_n$ converges in distribution to a normal variable $S$.
In the present paper we derive several explicit upper bounds for quantities of
the type $|\E[h(S_n)] -\E[h(S)]|$, where $h$ is a sufficiently smooth test
function. Our methods are based on Malliavin calculus, on interpolation
techniques and on the Stein's method for normal approximation. The bounds
deduced in our paper depend only on $Var[f^2(X_1)]$ and on simple infinite
series involving the components of $r$. In particular, our results generalize
and refine some classic CLTs by Breuer-Major, Giraitis-Surgailis and Arcones,
concerning the normal approximation of partial sums associated with
Gaussian-subordinated time-series.
