Bootstrap Tests for an Autoregressive Unit Root in the Presence of Weakly Dependent Errors

Abstract

This paper examines bootstrap tests of the null hypothesis of an autoregressive unit root in models that may include a linear rend and/or an intercept and which are driven by innovations that belong to the class of stationary and invertible linear processes. Our approach makes use of a sieve bootstrap procedure based on residual resampling from autoregressive approximations, the order of which increases with the sample size at a suitable rate. We show that the sieve bootstrap provides asymptotically valid tests of the unit‐root hypothesis and demonstrate the small‐sample effectiveness of the method by means of simulation.