  In this article, we show that a general class of weakly stationary time
series can be modeled applying Gaussian subordinated processes. We show that,
for any given weakly stationary time series $(z_t)_{z\in\mathbb{N}}$ with given
equal one-dimensional marginal distribution, one can always construct a
function $f$ and a Gaussian process $(X_t)_{t\in\mathbb{N}}$ such that
$\left(f(X_t)\right)_{t\in\mathbb{N}}$ has the same marginal distributions and,
asymptotically, the same autocovariance function as $(z_t)_{t\in\mathbb{N}}$.
Consequently, we obtain asymptotic distributions for the mean and
autocovariance estimators by using the rich theory on limit theorems for
Gaussian subordinated processes. This highlights the role of Gaussian
subordinated processes in modeling general weakly stationary time series. We
compare our approach to standard linear models, and show that our model is more
flexible and requires weaker assumptions.
