Asymptotics for the residual-based bootstrap approximation in nearly nonstationary AR(1) models with possibly heavy-tailed innovations

Consider a nearly nonstationary AR(1) model, Xt=θnXt−1+ut, where θn=1−γ/n, γ is a fixed constant, and the innovations are in the domain of attraction of the normal law with possibly infinite variance. As for the least squares estimator θˆn of θn, we propose to use a residual-based m-out-of-n bootstrap procedure to approximate the distribution of θˆn−θn, and its asymptotic validity is proved.