Bootstrap unit root tests for time series with non-stationary volatility

The presence of permanent volatility shifts in key macroeconomic and financial variables in developed economies appears to be relatively common. Conventional unit root tests are unreliable in the presence of such behavior, having nonpivotal asymptotic null distributions. In this paper we propose a bootstrap approach to unit root testing that is valid in the presence of a wide class of permanent variance changes that includes single and multiple (abrupt and smooth transition) volatility change processes as special cases. We make use of the so-called wild bootstrap principle, which preserves the heteroskedasticity present in the original shocks. Our proposed method does not require the practitioner to specify any parametric model for the volatility process. Numerical evidence suggests that the bootstrap tests perform well in finite samples against a range of nonstationary volatility processes.