A joint test for structural stability and a unit root in autoregressions

A test of the joint null hypothesis of parameter stability and a unit root within an ADF style autoregressive specification whose entire parameter structure is potentially subject to a structural break at an unknown time period is developed. The proposed test is a useful diagnostic tool for assessing the interactions of breaks and unit root type of nonstationarities in time series, in addition to offering a powerful device for detecting changes in persistence. As a byproduct the limiting behaviour of a related Wald statistic designed to test solely the null of parameter stability in an environment with a unit root is also obtained. These distributions are free of nuisance parameters and easily tabulated. The finite sample properties of the tests are assessed through a series of simulations, and an application to macroeconomic data illustrates their usefulness.