Estimation of Linear Regression Models with Serially Correlated Errors

Abstract

This paper develops a generalized least squares (GLS) estimator in a linear regression model with serially correlated errors. In particular, the asymptotic optimality of the proposed estimator is established. To ob- tain this result, we use the modied Cholesky decomposition to estimate the inverse of the error covariance matrix based on the ordinary least squares (OLS) residuals. The resulting matrix estimator maintains positive denite- ness and converges to the corresponding population matrix at a suitable rate. The outstanding nite sample performance of the proposed GLS estimator is illustrated using simulation studies and two real datasets.