A Simple Unit Root Test For Near Double-Integrated Time Series

Abstract

We consider the problem of testing for unit root in time series where the error term of the series is near unit root. As the error term approaches unit root, existing tests no longer retain reasonable small sample properties. We introduce a test statistic that is well-behaved in small sample under such condition. Empirical applications reject the unit root null hypothesis for macroeconomic series, such as unemployment and consumer prices, where conventional unit root tests have been unable to do so.