The Structure of Generalized Linear Dynamic Factor Models

In this contribution we present a structure theory for generalized linear dynamic factor models. Generalized dynamic factor models have been proposed approximately a decade ago for modeling of high dimensional time series where the cross sectional dimension is of the same order of magnitude as the sample size. In these models the classical assumption for factor models, that the noise components are mutually uncorrelated, is relaxed by allowing for weak dependence. Structure theory turns out to be important for estimation and model selection. The results obtained heavily draw from linear system theory. The contribution consists of two main parts. In the first part we deal with “denoising”, i.e. with getting rid of the noise in the observations. In the second part we deal with constructing linear dynamic systems for the latent variables. Here an important result is the generic zerolessness of the transfer function relating the latent variables and the dynamic factors. This allows for modeling the latent variables by (singular) autoregressions which simplifies estimation.