• Autoregressive approximation;
  • hypothesis testing;
  • linear process;
  • sieve bootstrap;
  • unit root

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.