  In this paper we introduce a modified version of a gaussian standard
first-order autoregressive process where we allow for a dependence structure
between the state variable $Y_{t-1}$ and the next innovation $\xi_t$. We call
this model dependent innovations gaussian AR(1) process (DIG-AR(1)). We analyze
the moment and temporal dependence properties of the new model. After proving
that the OLS estimator does not consistently estimate the autoregressive
parameter, we introduce an infeasible estimator and we provide its
$\sqrt{T}$-asymptotic normality.
