  In this paper, we consider the usual linear regression model in the case
where the error process is assumed strictly stationary. We use a result from
Hannan (1973), who proved a Central Limit Theorem for the usual least square
estimator under general conditions on the design and on the error process.
Whatever the design satisfying Hannan's conditions, we define an estimator of
the covariance matrix and we prove its consistency under very mild conditions.
As an application, we show how to modify the usual tests on the linear model in
this dependent context, in such a way that the type-I error rate remains
asymptotically correct, and we illustrate the performance of this procedure
through different sets of simulations.
