An Alternative to the Bounds Test for Testing for Serial Correlation in Least-Squares Regression

This article shows how to transform residuals from regression on an arbitrary set of k regressors to a set of values having the same joint distribution as the residuals from regression on a different set L of k regressors. Let d′ denote the value of the statistic <tex-math>\Σ (zₜ-zₜ₋₁)²/\Σ zₜ²</tex-math> calculated from these values. It is shown that for a suitable choice of L the distribution of d′ is the same as that of <tex-math>dU</tex-math>, the significance values of which are tabulated in [1].