Asymptotic Distribution of Least Squares Estimators for Linear Models with Dependent Errors: Regular Designs

We consider the usual linear regression model in the case where the error process is assumed strictly stationary.We use a result of Hannan, who proved a Central Limit Theorem for the usual least squares estimator under general conditions on the design and the error process.We show that for a large class of designs, the asymptotic covariance matrix is as simple as in the independent and identically distributed (i.i.d.) case.We then estimate the covariance matrix using an estimator of the spectral density whose consistency is proved under very mild conditions.