ESTIMATORS OF PARAMETERS OF LINEAR MODELS WITH AUTO CORRELATED DISTURBANCES IN ORDINARY LEAST SQUARES (OLS)

Uchendu, Bartholomew A. & Ibeh Gabreil C

Department of Maths/Statistics

Federal Polytechnic, Nekede Owerri, Nigeria

Email: Uchendubartholomew@yahoo.com; gabmicchuks@yahoo.com

ABSTRACT

The consequences of applying Ordinary Least Squares to a relationship with autocorrected disturbances are qualitatively similar to those already derived for the heteroscedastic case, namely unbiased but inefficient estimation and invalid inference procedures. As in the case of heteroscedasticity, in the presence of autocorrelation, the Ordinary Least Square estimators are still linear unbiased as well as consistent and asymptotically normally distributed, but they are no longer efficient (ie, minimum variance). In the case of heteroscedasticity, we distinguish two cases and the possible cause and sources of autocorrelation. The violation of the assumptions of normality may have significant consequences in applying Ordinary Least Squares and such consequences include substantial loss in efficiency, inflating the precision or accuracy of the estimators by underestimating the standard error of β. Moreover, violating of the assumptions of normally of the error term is important in econometric analysis. If this assumption is violated, then the basis of hypothesis testing breaks down. In this direction, a large number of possible tests for normality and robust estimator have been suggested. The assumption of lack of autocorrelation or serial correlation of the error term implies that the disturbance covariance at all possible pairs of observation points are zero. Violation provides the basis of for this research because it affects the consistency of the Ordinary Least Square estimators. Models with such disturbances are widespread, as applied econometrics especially in modeling of economic data.

Keywords: Least squares, Estimator, OLS, Minimum Variance, and Error Term