JDS Journal of Data Science 1683-86021680-743X1680-743X School of Statistics, Renmin University of China JDS1108 10.6339/23-JDS1108 Statistical Data Science Revisiting the Use of Generalized Least Squares in Time Series Regression Models FangYuefyue@ceibs.edu1∗ KoreishaSergio G.2 ShaoQi-man3 Department of Economics and Decision Sciences, China International Business School, Shanghai, P.R. China Lundquist College of Business, University of Oregon, Eugene, OR, USA Department of Statistics and Data Science, Southern University of Science and Technology, Shenzhen, P.R. China Corresponding author. Email: fyue@ceibs.edu. 20242172023224486504 Supplementary Material

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3120231062023 2024 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.2024 Open access article under the CC BY license.

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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