TY - JOUR

T1 - Revisiting the Use of Generalized Least Squares in Time Series Regression Models

AU - Fang, Yue

AU - Koreisha, Sergio G.

AU - Shao, Qi-man

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

UR - https://www.mendeley.com/catalogue/f100263c-bc05-3f6f-a4fd-7c426e9afb3e/

U2 - 10.6339/23-jds1108

DO - 10.6339/23-jds1108

M3 - Journal

SN - 1683-8602

SP - 1

EP - 19

JO - Journal of Data Science

JF - Journal of Data Science

ER -