Bootstrap test of significance and sequential bootstrap estimation for unstable first order autoregressive processes

Abstract

The asymptotic validity of the bootstrap for a test of criticality in a first order autoregressive, AR(1) process is established. To circumvent the asymptotic invalidity of the standard bootstrap least squares estimator for the unstable case, a sequential bootstrap procedure for the estimation of the parameter β in the AR(1) model, is studied. The asymptotic validity of the sequential bootstrap estimator is established for all |β|≤1.