Variation Comparison of OLS and GLS Estimators using Monte Carlo Simulation of Linear Regression Model with Autoregressive Scheme

Abstract

In this research we discusses to Ordinary Least Squares and Generalized Least Squares techniques and estimate with First Order Autoregressive scheme from different correlation levels by using simple linear regression model. A comparison has been made between these two methods on the basis of variances results. For the purpose of comparison, we use simulation of Monte Carlo study and the experiment is repeated 5000 times. We use sample sizes 50, 100, 200, 300 and 500, and observe the influence of different sample sizes on the estimators.

By comparing variances of OLS and GLS at different values of sample sizes and correlation levels with , we found that variance of ( ) at sample size 500, OLS and GLS gives similar results but at sample size 50 variance of GLS ( ) has minimum values as compared to OLS. So it is clear that variance of GLS ( ) is best. Similarly variance of ( ) from OLS and GLS at sample size 500 and correlation -0.05 with , GLS give minimum value as compared to all other sample sizes and correlations.

By comparing overall results of Ordinary Least Squares (OLS) and Generalized Least Squares (GLS), we conclude that in large samples both are gives similar results but small samples GLS is best fitted as compared to OLS.