Testing the null of stationarity in the presence of structural breaks for multiple time series

This paper introduces various consistent tests for the null hypothesis of stationarity with possibly unknown multiple structural break points against the alternative of nonstationarity that can be applied to multiple as well as univariate time series. These tests can be applied to either partial or pure structural breaks. It is shown that tests for stationarity become divergent when structural breaks are ignored. We show that we can allow a variety of structural breaks for which limiting distributions are derived and tabulated. Finite sample properties are studied by simulation. We also consider multivariate testing strategy and univariate tests and find that multivariate tests are often more powerful than univariate tests.