Bootstrapping unit root tests for autoregressive time series

Abstract

The theory developed for bootstrapping unit root tests in an autoregressive (AR) context has been concerned mainly with the large-sample behavior of the methods proposed under the assumption that the null hypothesis is true. No results exist for the relative performance and the power behavior of the bootstrap methods under the alternative. This article studies the properties of different AR bootstrap schemes of the unit root hypothesis, including a new proposal based on unrestricted residuals. It shows that bootstrap procedures based on differencing the observed series suffer from power problems as compared with bootstrap procedures based on unrestricted residuals. Whereas for finite-order AR processes differencing leads to just a loss of power, for infinite-order autoregressions such a differencing makes the application of sieve AR bootstrap schemes inappropriate if the alternative is true. The superiority of the new bootstrap proposal is shown, and some numerical examples illustrate our theoretical findings. © 2005 American Statistical Association.