The quest for unified solution for handling multicollinearity and autocorrelation jointly has resulted in a great deal of interest in two-stage approaches within the linear modelling paradigm recently. This paper contributes to this growing interest with Two-Stage Ridge Quantile Regression (TRQR) and Two-Stage Lasso Quantile Regression (TLQR) methods. The two-stage methods fundamentally involve the application of appropriate transformation to linear regression data followed by regularization to control respectively, autocorrelation and multicollinearity. The aim is to determine if regularized and robust regression methods reduce total model error, and find which method is most effective for dealing with autocorrelation and multicollinearity problems. The utility of the methods were assessed using simulations based on models with small (2) to relatively large (8) predictors, in comparison with other regression methods using the Mean Squared Error criterion. The results indicate that the TRQR method, at 0.5 quantile level, is most suitable for handling multicollinearity and autocorrelation problems with many (8 or more) predictor variables. However, the Two-Stage Ridge Regression method performs better with few (2 or less) predictor variables. The findings show that each method is affected by sample size, number of predictors or multicollinearity level.

Autocorrelation, Multicollinearity, Two-Stage method, Ridge regression, Lasso regression, Mean squared error