Improved Beta Approximation to the Critical Point of the Durbin-Watson Test Statistic

Abstract

The Durbin-Watson test in linear regression models is widely known to have problems in its application. The problem of the calculation burden in the exact test and that of the inconclusive region in the bounds test have motivated several approximations to the exact critical point. This paper improves upon the beta approximation by considering that the range of the Durbin-Watson statistic obtainable a priori is reducible to a subinterval of [0,4], which Durbin and Watson (1951) assumed when devising their beta approximation. The proposed approximation is found to outperform the beta, a +bd, and Jeong's approximations. Its computational burden is virtually the same as that of Beta, heavier than those of a +bd, and Jeong's. However, the additional burden of computing beta critical points is removed if one uses either our tables or built-in inverse beta function.