In this article, we study and compare the properties of several bootstrap unit-root tests recently proposed in the literature. The tests are dickey–fuller (df) or augmented df, based either on residuals from an autoregression and the use of the block bootstrap or on first-differenced data and the use of the stationary bootstrap or sieve bootstrap. We extend the analysis by interchanging the data transformations (differences vs. Residuals), the types of bootstrap and the presence or absence of a correction for autocorrelation in the tests.we show that two sieve bootstrap tests based on residuals remain asymptotically valid. In contrast to the literature which focuses on a comparison of the bootstrap tests with an asymptotic test, we compare the bootstrap tests among themselves using response surfaces for their size and power in a simulation study.this study leads to the following conclusions: (i) augmented df tests are always preferred to standard df tests; (ii) the sieve bootstrap performs better than the block bootstrap; (iii) difference-based tests appear to have slightly better size properties, but residual-based tests appear more powerful.
Palm, F. C., Smeekes, S., & Urbain, J. R. Y. J. (2008). Bootstrap Unit Root Tests: comparison and extensions. Journal of Time Series Analysis, 29, 370-401. https://doi.org/10.1111/j.1467-9892.2007.00565.x