Testing the null of difference stationarity against the alternative of a stochastic unit root: A new test based on multivariate STUR

Abstract A multivariate stochastic unit root process is used to test a simple versus a stochastic unit root. The score statistic and its asymptotic distribution under the null are given, and the test is seen to have a very acceptable power function. Simulations are performed to assess the robustness of the procedure in two common circumstances: preselecting the autoregressive order for the series using Akaike’s Information Criterion, and allowing for an MA component. An empirical application to macroeconomic and financial series is given to illustrate the test and to compare it to the main alternatives in the literature.