Bootstrap-Assisted Unit Root Testing With Piecewise Locally Stationary Errors

TL;DR

This paper develops a bootstrap method for unit root testing in models with piecewise locally stationary errors, accommodating complex nonstationary error structures with smooth and abrupt changes.

Contribution

It introduces a dependent wild bootstrap approach for non-pivotal null distributions in unit root tests with nonstationary errors, with theoretical validation and practical comparisons.

Findings

Bootstrap method accurately approximates null distributions.

Proposed approach outperforms recolored wild bootstrap in simulations.

Method demonstrates validity in nonstationary error settings.

Abstract

In unit root testing, a piecewise locally stationary process is adopted to accommodate nonstationary errors that can have both smooth and abrupt changes in second- or higher-order properties. Under this framework, the limiting null distributions of the conventional unit root test statistics are derived and shown to contain a number of unknown parameters. To circumvent the difficulty of direct consistent estimation, we propose to use the dependent wild bootstrap to approximate the non-pivotal limiting null distributions and provide a rigorous theoretical justification for bootstrap consistency. The proposed method is compared through finite sample simulations with the recolored wild bootstrap procedure, which was developed for errors that follow a heteroscedastic linear process. Further, a combination of autoregressive sieve recoloring with the dependent wild bootstrap is shown to perform well. The validity of the dependent wild bootstrap in a nonstationary setting is demonstrated for the first time, showing the possibility of extensions to other inference problems associated with locally stationary processes.