Testing in unobserved components models

This article reviews recent work on testing for the presence of non-stationary unobserved components and presents it in a unified way. Tests against random walk components and seasonal components are given and it is shown how the procedures may be extended to multivariate models and models with structural breaks. Many of the test statistics have an asymptotic distribution belonging to the class of generalized Cramér–von Mises distributions. A test for the number of common trends, or equivalently, co-integrating vectors, is also described.