Revisiting the Use of Generalized Least Squares in Time Series Regression Models
Volume 22, Issue 4 (2024), pp. 486–504
Pub. online: 21 July 2023
Type: Statistical Data Science
Open Access
Open Access
Received
3 January 2023
3 January 2023
Accepted
10 June 2023
10 June 2023
Published
21 July 2023
21 July 2023
Abstract
Linear regression models are widely used in empirical studies. When serial correlation is present in the residuals, generalized least squares (GLS) estimation is commonly used to improve estimation efficiency. This paper proposes the use of an alternative estimator, the approximate generalized least squares estimators based on high-order AR(p) processes (GLS-AR). We show that GLS-AR estimators are asymptotically efficient as GLS estimators, as both the number of AR lag, p, and the number of observations, n, increase together so that $p=o({n^{1/4}})$ in the limit. The proposed GLS-AR estimators do not require the identification of the residual serial autocorrelation structure and perform more robust in finite samples than the conventional FGLS-based tests. Finally, we illustrate the usefulness of GLS-AR method by applying it to the global warming data from 1850–2012.
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