Effect of Multicolinearity and Autocorrelation on Predictive Ability of Some Estimators of Linear Regression Model

Abstract

Violation of the assumptions of independent regressors and error terms in linear regression model has respectively resulted into the problems of multicollinearity and autocorrelation. Each of these problems separately has significant effect on parameters estimation of the model parameters and hence prediction.  This paper therefore attempts to investigate the joint effect of the existence of multicollinerity and autocorrlation on Ordinary Least Square (OLS) estimator, Cochrane-Orcutt (COR) estimator, Maximum Likelihood (ML) estimator and the estimators based on Principal Component (PC) analysis on prediction of linear regression model through Monte Carlo studies using the adjusted coefficient of determination goodness of fit statistic of each estimator. With correlated normal variables as regressors, it further identifies the best estimator for prediction at various levels of sample sizes (n), multicollinearity  and autocorrlation . Results reveal the pattern of performances of COR and ML at each level of multicollinearity over the levels of autocorrelation to be generally and evidently convex especially when  and while that of OLS and PC is generally concave. Moreover, the COR and ML estimators perform equivalently and better; and their performances become much better as multicollinearity increases. The COR estimator is generally the best estimator for prediction except at high level of multicollinearity and low levels of autocorrelation. At these instances, the PC estimator is either best or competes with the COR estimator. Moreover, when the sample size is small (n=10) and multicollinearity level is not high, the OLS estimator is best at low level of autocorrelation whereas the ML is best at moderate levels of autocorrelation.

.Keywords: Prediction, Estimators, Linear Regression Model, Multicollinearity, Autocorrelation.