The relative efficiency of OLS in the linear regression model with spatially autocorrelated errors

1993 ◽  
Vol 34 (1) ◽  
pp. 263-270 ◽  
Author(s):  
C. Tilke
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Relative Efficiency ◽  
Autocorrelated Errors

scholarly journals On Least Squares Estimation in a Simple Linear Regression Model with Periodically Correlated Errors: A Cautionary Note

2016 ◽  
Vol 41 (3) ◽  
Author(s):  
Abdullah A. Smadi ◽  
Nour H. Abu-Afouna
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Least Squares ◽  
Autoregressive Model ◽  
Relative Efficiency ◽  
Generalized Least Squares ◽  
Correlated Errors ◽  
Simple Linear Regression ◽  
Simple Regression Model ◽  
Autocorrelated Errors

In this research the simple linear regression (SLR) model with autocorrelated errors is considered. Traditionally, correlated errors are assumed to follow the autoregressive model of order one (AR(1)). Beside this model we will also study the SLR model with errors following the periodic autoregressive model of order one (PAR(1)). The later model is useful for modeling periodically autocorrelated errors. In particular, it is expected to beuseful when the data are seasonal. We investigate the properties of the least squares estimators of the parameters of the simple regression model when the errors are autocorrelated and for various models. In particular, the relative efficiency of those estimates are obtained and compared for the white noise, AR(1) and PAR(1) models. Also, the generalized least squares estimates for the SLR with PAR(1) errors are derived. The relative efficiency of the intercept and slope estimates based on both methods is investigated via Monte-Carlo simulation. An application on real data set is also provided.It should be emphasized that once there are sufficient evidences that errors are autocorrelated then the type of this autocorrelation should be uncovered. Then estimates of model’s parameters should be obtained accordingly, using some method like the generalized least squares but not the ordinary least squares.

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