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Linear regression models are useful statistical tools to analyze data sets inseveral different fields. There are several methods to estimate the parametersof a linear regression model. These methods usually perform under normallydistributed and uncorrelated errors with zero mean and constant variance.However, for some data sets error terms may not satisfy these or some of theseassumptions. If error terms are correlated, such as the regression models withautoregressive (AR(p)) error terms, the Conditional Maximum Likelihood (CML)under normality assumption or the Least Square (LS) methods are often used toestimate the parameters of interest. For CML estimation a distributionalassumption on error terms is needed to carry on estimation, but, in practice,such distributional assumptions on error terms may not be plausible. Therefore,in such cases some alternative distribution free methods are needed to conductthe parameter estimation. In this paper, we propose to estimate the parametersof a linear regression model with AR(p) error term using the EmpiricalLikelihood (EL) method, which is one of the distribution free estimationmethods. A small simulation study and a numerical example are provided toevaluate the performance of the proposed estimation method over the CML method.The results of simulation study show that the proposed estimators based on ELmethod are remarkably better than the estimators obtained from the CML methodin terms of mean squared errors (MSE) and bias in almost all the simulationconfigurations. These findings are also confirmed by the results of thenumerical and real data examples.

Empirical Likelihood Estimation for Linear Regression Models with AR(p) Error Terms