Feasible GLS for time series regression

原文摘要

We consider GLS and OLS estimation in a linear regression model with serially correlated errors, and we provide the following contributions. First, we clarify when OLS is consistent or not. Second, we give sufficient conditions such that GLS is valid without the assumption of exogenous regressors (uncorrelated with past innovations). Third, we devise a feasible GLS procedure valid whether or not the regressors are exogenous, and which achieves a MSE close to that of the correctly specified infeasible GLS. Fourth, we derive the asymptotic distribution of this feasible GLS estimate: with exogenous regressors, the limit distribution is the same as that of the infeasible GLS estimator. However, with non-exogenous regressors, an additional term is present in the asymptotic variance. We provide a variance estimator, free of tuning parameters, which delivers confidence intervals with asymptotically correct coverage in both cases. We also illustrate how GLS can be more robust than OLS when the regressors are exogenous, even when GLS is based on an incorrect correction. The main assumptions are: a) the regressors are pre-determined (uncorrelated with future innovations); b) the errors are stationary thereby admitting a Wold representation in terms of some unpredictable innovations; c) the moving-average representation of the errors is invertible and implies a short-memory process. We also briefly address issues related to heteroskedastic errors.

摘要来源：ScienceDirect · 出版社摘要