Large-sample inference in the general AR(1) model

Abstract

The situation where the available data arise from a general AR(1) model is discussed, and two new avenues for constructing confidence intervals for the unknown autoregressive root are proposed, one based on a Central Limit Theorem, and the other based on the block-bootstrap. The two new methodologies rely on clever preprocessing of the original series, and are subsequently free of the difficulties present in previous methods that were due to data nonstationarity and/or discontinuity in the limit distribution in the case of a unit root. Some finite-sample simulations are also presented supporting the applicability of the proposed methods, and the problem of bootstrap block size choice is discussed.