On the finite-sample power of modified Dickey-Fuller tests: The role of the initial condition

The relationship between the initial condition of time series data and the power of the Dickey-Fuller (1979) test and a number of modified Dickey-Fuller tests is examined. The results obtained extend the asymptotic analysis of Muller and Elliott (2003) by both focussing upon finite-sample power and examining previously unconsidered modified tests. It is shown that deviation of the initial condition from the underlying deterministic component of a time series increases the finite-sample power of the original Dickey-Fuller test, but removes the potential gains in power resulting from the use of modified tests. Interestingly, some variation in the properties of modified tests is noted. In addition to allowing evaluation of previous Monte Carlo studies of the finite-sample power of unit root tests, the results presented allow practitioners to select, and interpret the results of, alternative unit root tests in light of the initial condition of the data examined.