System Identification by Dynamic Factor Models

This paper concerns the modelling of stochastic processes by means of 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. One of the central questions in this paper is how uncertainty about the noise structure translates into non-uniqueness of the possible underlying latent processes. We investigate several possible noise specifications and analyse properties of the resulting class of observationally equivalent factor models. This concerns in particular the characterization of optimal models and properties of continuity and consistency.