The power of autocorrelation tests near the unit root in models with possibly mis-specified linear restrictions

It is well known that the Durbin–Watson and several other tests for first-order autocorrelation have limiting power of either zero or one in a linear regression model without an intercept, and a constant lying strictly between these values when an intercept term is present. This paper considers the limiting power of these tests in models with possibly incorrect restrictions on the coefficients. It is found that with linear restrictions on the coefficients, the limiting power can still drop to zero even with the inclusion of an intercept in the regression. Our results also accommodate the situation of a possibly mis-specified linear model.