Unit root test in a threshold autoregression: asymptotic theory and residual-based block bootstrap

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+