Generalized Linear Dynamic Factor Models: An Approach via Singular Autoregressions

We consider generalized linear dynamic :factor models. These models have been developed recently and they are used for high dimensional time series in order to overcome the curse of dimensionality. We present a structure theory with emphasis on the zeroless case, which is generic in the setting considered. Accordingly the latent variables are modeled as a possibly singular autoregressive process and (generalized) Yule Walker equations are used for parameter estimation. The Yule Walker equations do not necessarily have a unique solution in the singular case, and the resulting complexities are examined with a view to find a stable and coprime system.