Testing parameter constancy in unit root autoregressive models against continuous change

In this paper we derive tests for parameter constancy when the data generating process is non-stationary against the hypothesis that the parameters of the model change smoothly over time. To obtain the asymptotic distributions of the tests we generalize many theoretical results, as well as new are introduced, in the area of unit roots. The results are derived under the assumption that the error term is a strong mixing. Small sample properties of the tests are investigated, and in particular, the power performances are satisfactory.