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

https://doi.org/0012-9682(197005)38:3<422:AATTBT>2.0.CO;2-Y
p. 422-429

J. Durbin

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 $d^{\prime}$ denote the value of the statistic $\Sigma (z_1 - z_{t-1})^2/ \Sigma z{_t}{^z}$ calculated from these values. It is shown that for a suitable choice of $L$ the distribution of $d^{\prime}$ is the same as that of $d_v$, the significance values of which are tabulated in [$\textbf{1}$].