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

Hrishikesh D. Vinod

Fordham University - Department of Economics

March 21, 2014

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.

Number of Pages in PDF File: 9

Keywords: Serially correlated errors, scalar covariance, regression

JEL Classification: C20, C15, C88

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Date posted: March 23, 2014  

Suggested Citation

Vinod, Hrishikesh D., Theil's BLUS Residuals and R Tools for Testing and Removing Autocorrelation and Heteroscedasticity (March 21, 2014). Available at SSRN: http://ssrn.com/abstract=2412740 or http://dx.doi.org/10.2139/ssrn.2412740

Contact Information

Hrishikesh D. Vinod (Contact Author)
Fordham University - Department of Economics ( email )
Dealy Hall
Bronx, NY 10458
United States
718-817-4065 (Phone)
718-817-3518 (Fax)
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