This rejoinder highlights some of the differences in the test approach adopted by Fernandez-Macho (2013) in his critique of Leong and Huang (2010) and those commonly found in the literature such as Granger and Newbold(1974), Phillips (1986) and Leong and Huang (2010)

We develop novel multivariate state-space models wherein the latent states evolve on the Stiefel manifold and follow a conditional matrix Langevin distribution. The latent states correspond to time-varying reduced rank parameter matrices, like the loadings in dynamic factor models and the...