The Properties of Procedures Dealing with Uncertainty about Intercept and Deterministic Trend in Unit Root Testing

The classic Dickey-Fuller unit-root test can be applied using three different equations, depending upon the inclusion of a constant and/or a time trend in the regression equation. This paper investigates the size and power properties of a unit-root testing strategy outlined in Enders (2004), which allows for repeated testing of the unit root with the three equations depending on the significance of various parameters in the equations. This strategy is similar to strategies suggested by others for unit root testing. Our Monte Carlo simulation experiments show that serious mass significance problems prevail when using the strategy suggested by Enders. Excluding the possibility of unrealistic outcomes and using a priori information on whether there is a trend in the underlying time series, as suggested by Elder and Kennedy (2001), reduces the mass significance problem for the unit root test and improves power for that test. Subsequent testing for whether a trend exists is seriously affected by testing for the unit root first, however.