Small-disturbance asymptotics and the Durbin-Watson and related tests in the dynamic regression model

Until recently, it was thought inappropriate to apply the Durbin-Watson (DW) test to a dynamic linear regression model because of the lack of appropriate critical values. Recently, Inder (1986) used a modified small-disturbance distribution (SDD) to find approximate critical values. This paper studies the exact SDD of statistics of the same general form as the DW statistic and suggests some changes to Inder's result. We show how to calculate true small-disturbance critical values and bounds for these critical values that take into account the exogenous regressors. Our results give a justification for the use of the familiar tables of bounds when the DW test is applied to a dynamic regression model.