Unit Root Testing via the Continuous-Path Block Bootstrap

A new resampling procedure, the continuous-path block bootstrap, is proposed in the context of testing for integrated (unit root) time series. The continuous-path block bootstrap (CBB) is a nonparametric procedure that successfully generates unit root integrated pseudo time series retaining the important characteristics of the data, e.g., the dependence structure of the stationary process driving the random walk. As a consequence, the CBB can accurately capture the distribution of many unit root test statistics. Large sample theory for the new bootstrap methodology is developed and the asymptotic validity of CBB-based unit root testing is shown via a bootstrap functional limit theorem. Applications of the new procedure to least squares and Dickey-Fuller type test statistics of the unit root hypothesis are given. Finite-sample simulations confirm a good alpha-level accuracy and an increased power associated with CBB-based unit root testing.