Generalized Least Squares Transformation with the Second-order Autoregressive Error

Abstract

The major problem found in the fitted simultaneous equations model (SEM) maybe the autocorrelation and/or moving average problems. These problems have an affect on the ordinary least squares (OLS) estimators are not efficient. A generalized least squares (GLS) transformation matrix in order to correct the second-order autocorrelation [AR(2)] is proposed in this article by using the Cholesky decomposition and also shown in theoretically and empirically, it is a correction of AR(2) problem. The simulation study shows that the AR(2) problem in the errors makes the values of sum squared error (SSE) higher than they should because the estimated values of the residuals still overestimate.