Variance ratio tests for a unit root in the presence of a mean shift: small sample properties and an application to purchasing power parity

Abstract

This study proposes a unit root test for a time series having a mean shift at an unknown point. The proposed test using a variance ratio as a test statistic can be used to test a wide range of linear and nonlinear processes characterized by a mean shift. Monte Carlo simulations indicate that our tests are more powerful than Dickey–Fuller type tests in regard to linear and nonlinear processes. When the test is applied to the Japanese real exchange rate, the empirical results show strong evidence that the Japanese real exchange rate has a stationary process around a mean shift.