Rank Based Dickey–Fuller Test Statistics

This article provides various comprehensive comparisons between Breitung–Gouriéroux and Granger–Hallman rank statistics for the unit root test. New analytical asymptotic properties for the Granger–Hallman rank statistic are demonstrated. The statistic is of a Dickey–Fuller type, where the observations are replaced with their rank counterparts. Weak convergence results are given for the nonstationary random walk process when the errors are assumed to have higher than two moments. Empirical percentiles of both Breitung–Gouriéroux and Granger–Hallman rank statistics are presented for different sample sizes. In addition, empirical powers and sizes for these rank statistics and for the Dickey–Fuller test statistic are shown for different distributions of the error terms.