CONSEQUENCES OF VIOLATING THE ASSUMPTIONS OF OLS IN THE PRESENCE OF AUTOCORRELATION

Uchendu, Bartholomew .A.

Department of Maths/Statistics

Federal Polytechnic, Nekede, Owerri, Nigeria

E-mail: uchendubartholomew@yahoo.com

Abstract: The consequences of applying OLS 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 OLS estimators are still linear unbiased as well as consistent and asymptotically normally distributed, but they are no longer efficient (i.e., 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 OLS 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 OLS estimators. Models with such disturbances are widespread, as applied econometrics especially in modeling of economic data.