A New Efficiency Rate for OLS and GLS Estimators in Time-Series Regressions

• Activity Number: 248
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Jaechoul Lee*+ and Robert B. Lund
• Companies: Boise State University and Clemson University
• Keywords: Asymptotic variance ; Autoregression ; Convergence rate ; Efficiency ; Simple linear regression ; Time series

Abstract

When a straight line is fitted to data with autocorrelated errors, generalized least squares estimators of the trend slope and intercept are attractive as they are unbiased and of minimum variance. However, computing generalized least squares estimators is laborious as their form depends on the autocovariances of the regression errors. On the other hand, ordinary least squares estimators are easy to compute and do not involve error autocovariances. It has been known for 50 years that ordinary and generalized least squares estimators have the same asymptotic variance when the errors are second order stationary. Hence, little precision is gained by using generalized least squares estimators in stationary error settings. This paper revisits this classical issue, deriving explicit expressions for the generalized least squares estimators and their variances when the regression errors are an autoregressive process. These expressions are then used to show that ordinary least squares methods are even more efficient than previously thought. Specifically, we show that the convergence rate of variance differences is one polynomial degree higher than previously explained.