The Limit Distribution of the Bootstrap for the Unit Root Test Statistic when the Residuals are Dependent

In this article, the unit root test for the AR(1) model with dependent residuals is considered. We adopt a bootstrap procedure to bootstrap the residuals with bootstrap sample size m less than the size n of the original sample. Under the assumptions that m → ∞ and m/n → 0, the convergence in probability of the bootstrap distribution function is established. Research supported by National Natural Science Foundation of China (No. 10471126)