State-space models on the stiefel manifold with a new approach to nonlinear filtering

Abstract

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 parameters of cointegrating relations in vector error-correction models. The corresponding nonlinear filtering algorithms are developed and evaluated by means of simulation experiments.