UNIT ROOT TEST IN A THRESHOLD AUTOREGRESSION: ASYMPTOTIC THEORY AND RESIDUAL-BASED BLOCK BOOTSTRAP

Abstract

This paper develops a test of the unit root null hypothesis against a stationary threshold process. This testing problem is nonstandard and complicated because a parameter is unidentified and the process is nonstationary under the null hypothesis. We derive an asymptotic distribution for the test, which is not pivotal without simplifying assumptions. A residual-based block bootstrap is proposed to calculate the asymptotic p-values. The asymptotic validity of the bootstrap is established, and a set of Monte Carlo simulations demonstrates its finite-sample performance. In particular, the test exhibits considerable power gains over the augmented Dickey-Fuller (ADF) test, which neglects threshold effects.