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.

中文翻译：

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具有误差的线性模型的最小二乘估计的渐近分布：常规设计

在误差过程被假定为严格平稳的情况下，我们考虑通常的线性回归模型。我们使用Hannan的结果，他在设计和误差过程的一般条件下证明了通常最小二乘估计的中心极限定理。结果表明，对于一大类设计，渐近协方差矩阵就像在独立且均匀分布（iid）情况下一样简单。然后，我们使用频谱密度估计量估计协方差矩阵，该估计量的一致性在非常温和的条件下得到证明。