Theil's BLUS Residuals and R Tools for Testing and Removing Autocorrelation and Heteroscedasticity

Theil (1968) proposed a transformation of regression residuals so that they are best (minimizes the trace of its covariance matrix), linear, unbiased and subject to the constraint that its covariance matrix is scalar (BLUS) in the sense that it is proportional to the identity matrix. Despite their desirable theoretical properties Theil's tests for autocorrelation and heteroscedasticity using BLUS residuals are not much used by researchers, perhaps because of computational difficulties. My R program is checked against Ford (2008), who provides an example with implementations in Eviews and SAS software. Vinod (2010) suggests going beyond testing by making efficient adjustments to overcome the ill effects of non-scalar covariances. Links for R software to implement those tools are provided here near the end of the paper. I hope that my R software will help researchers fill a gap in the literature by studying the size and power of Theil's tests in comparison with other tests in the literature, and begin to focus on simultaneously overcoming these two common problems