A bootstrap approximation to a unit root test statistic for heavy-tailed observations

In the context of the AR(1) model with innovations in the domain of attraction of an alpha-stable law, we develop a residual bootstrap approximation to the distribution of a least-squares estimator of the autoregressive parameter when this parameter is equal to unity. Our procedure requires drawing bootstrap samples of size m < n, n being the size of the original sample. We establish the convergence in probability of the bootstrap distribution function assuming that m -> infinity and m/n -> 0. An analogous result is established for the partial sum process of the bootstrap noise sequence. (C) 2003 Elsevier Science B.V. All rights reserved.