System identification by dynamic factor models

This paper is concerned with linear dynamic factor models. In such models the observed process is decomposed into a structured part called the latent process, and a remainder that is called noise. The observed variables are treated in a symmetric way, so that no distinction between inputs and outputs is required. This motivates the condition that also the prior assumptions on the noise are symmetric in nature. We investigate the relation between optimal models and the spectrum of the observed process. This concerns in particular properties of continuity and consistency. Several possible noise specifications and measures of fit are considered.