State-space models on the Stiefel manifold with a new approach to nonlinear filtering - Yukai Yang; Luc Bauwens (Econometrics, 2018)
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.
Keywords: C32; C51; 330; state-space models; Stiefel manifold; matrix Langevin distribution; filtering; smoothing; Laplace method; dynamic factor model; cointegration