MONTE CARLO APPROACH FOR COMPARATIVE ANALYSIS OF REGRESSION TECHNIQUES IN THE PRESENCE OF MULTICOLLINEARITY AND AUTOCORRELATION PHENOMENA

Abstract

Multicollinearity and Autocorrelation are two very common problems in regression analysis. As its well-known, the presence of some degrees of multicollinearity results in estimation instability and model mis-specification while the presence of serial correlated errors lead to underestimation of the variance of parameter estimates and inefficient prediction. These two conditions have adverse effects on estimation and prediction; therefore, a wide range of tests have been developed to reduce their impact. Invariably, the multicollinearity and autocorrelation problems are dealt with separately in most studies. Thus, this study explored the predictive ability of the proposed GLS-Ridge regression on multicollinearity and autocorrelation problems simultaneously, using simulated dataset. Data used for the study was the data simulated using Monte Carlo. In the application, 1000 repetitions have been simulated for each of the sample size of . The model (GLS-Ridge), was proposed, and an estimator,  was derived. Least squares, ridge, lasso and the GLS-R model were applied to the simulated dataset. Regression coefficients for each estimator were computed and statistical comparison criteria; Mean Square Error and Akaike Information Criteria of the estimates were used to select the best model. For the simulated data, the GLS-R model had smaller AIC value than least squares, ridge regression and LASSO techniques for samples . Among these four techniques, the GLS-R model gives the smallest AIC value. The research work revealed that the GLS-R regression technique has a better predictive ability in the presence of autocorrelation and multicollinearity, hence it is preferred than the other three techniques.