Asian Journal of Mathematics & Statistics1994-54182077-2068Asian Network for Scientific Information10.3923/ajms.2008.14.23OlaomiJ.O.IfederuA.1200811Assumptions in the classical normal
linear regression model include that of lack of autocorrelation of the
error terms and the zero covariance between the explanatory variable and
the error terms. This study is channeled towards the estimation of the
parameters of the linear regression models when the above two assumptions
are violated. The study used the Monte-Carlo method to investigate the
performance of five estimators: Ordinary Least Squares (OLS), Cochrane
Orcutt (CORC), Hildreth Lu (HILU), Maximum Likelihood (ML) and Maximum
Likelihood Grid (MLGRID) in estimating the parameters of a single linear
regression model in which` the exponential explanatory variable is also
correlated with the autoregressive error terms. The simulation results,
under the finite sampling properties of bias, Variance and Root Mean Squared
Error (RMSE), show that all estimators are adversely affected as autocorrelation
coefficient (ρ) is close to unity. In this regard, the estimators
rank as follows in descending order of performance: OLS, MLGRID, ML, CORC
and HILU. The estimators conform to the asymptotic properties of estimates
considered. This is seen at all levels of autocorrelation and at all significant
levels. The estimators rank in decreasing order in conformity with the
observed asymptotic behaviour as follows: OLS, ML, MLGRID, HILU and CORC.
The results suggest that OLS should be preferred when autocorrelation
level is relatively mild (ρ = 0.4) and the exponential regressor
is significantly correlated at 5% with the autocorrelated error terms.]]>Beach, C.M. and J.S. Mackinnon,1978Busse, R., R. Jeske and W. Kramer,1994Butte, G.,2002Cochrane, D. and G.H. Orcutt,1949Durbin, J. and G.S. Watson,1950Durbin, J. and G.J. Watson,1951Durbin, J. and G.S. Watson,1971Hildreth, C. and J.Y. Lu,1960Ifederu, A.,2006Johnston, J.,1984Johnston, J. and J. DiNardo,1997Kleiber, C.,2001Kramer, W.,1980Kramer, W.,1998Kramer, W. and U. Hassler,1998Kramer, W. and F. Marmol,2002Maeshiro, A.,1976Nwabueze, J.C.,2000Nwabueze, J.C.,2005Nwabueze, J.C.,2005Olaomi, J.O.,2004Olaomi, J.O.,2007Olaomi, J.O. and A. Ifederu,2006Olaomi, J.O. and J.O. Iyaniwura,2006Park, R.E. and B.M. Mitchell,1980Rao, P. and Z. Griliches,1969TSP,2005