Testing for Unit Roots Using Forward and Reverse Dickey‐fuller Regressions

This article suggests a simple test for the null hypothesis that a process contains a unit root against a (trend) stationary alternative. It is based on the maximum value of the standard Dickey-Fuller tests when applied to both the forward and reverse data realizations. Thus, it requires no special computation and can easily be calculated from most existing econometric software packages. The null distribution of the maximum test is tabulated using Monte Carlo simulation and it is demonstrated to have considerably more power to reject the false null of a unit root than the standard Dickey-Fuller test. The tests are also shown to share very similar robustness properties. When applied to a number of well known U.S. macroeconomics time series, the new test rejects the unit root hypothesis more frequently than does the usual Dickey-Fuller test. Copyright 1995 by Blackwell Publishing Ltd