Bounded unit root processes with non-stationary volatility

This article concerns the unit root testing under nonstandard conditions for a time series process, such as having an innovation process with non-stationary variance and being limited inside an interval. These conditions are investigated separately in the unit root literature and shown to cause problems, such as size distortions. In this article, we consider the presence of both conditions in the unit root tests simultaneously. The simulation results indicate that the previous methods fail to provide satisfactory inference performance under the simultaneous presence of these conditions. To alleviate this issue, we propose a robust unit root testing mechanism and derive this procedure’s asymptotic properties.