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 non-stationarity that can be applied both to univariate and multiple time series, and both to partial or pure structural breaks. The paper shows that tests for stationarity become divergent when structural breaks are ignored. We also demonstrate that one can allow for 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.