Prediction Using Estimators of Linear Regression Model with Aurocorrelated Error Terms and Correlated Stochastic Uniform Regressors

Abstract

Prediction remains one of the fundamental reasons for regression analysis. However, the Classical Linear Regression Model is formulated under some assumptions which are not always satisfied especially in business, economic and social sciences leading to the development of many estimators. This work, therefore, attempts to examine the performances of the Ordinary Least Square estimator (OLS), Cochrane-Orcutt estimator (COR), Maximum Likelihood estimator (ML) and the estimators based on Principal Component analysis (PC) in prediction of linear regression model under the violations of assumption of non – stochastic regressors, independent regressors and error terms. With stochastic uniform variables as regressors, Monte - Carlo experiments were conducted over the levels of autocorrelation, correlation between regressors (multicollinearity -) and sample sizes, and best estimators for prediction purposes are identified using the goodness of fit statistics of the estimators. Results show that the performances of COR and ML at each level of multicollinearity over the levels of autocorrelation have a convex – like pattern while that of OLS, PR1 and PR2 are concave – like. Also, as the level of multicollinearity increases the estimators especially the COR and ML estimators perform much better at all the levels of autocorrelation. Furthermore, results show that except when the sample size is small (n=10), the performances of the COR and ML estimators are generally best and almost the same, even though at low level of autocorrelation the PC estimator either performs better than or competes with the best estimator when  and . When the sample size is small (n =10), the COR estimator is best except when the autocorrelation level is low and  or. At these instances, the PR2 estimator is best. Moreover, at low level of autocorrelation in all the sample sizes, the OLS estimator competes with the best estimator in all the levels of multicollinearity.

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