Singular Autoregressions for Generalized Dynamic Factor Models

We consider Generalized Linear Dynamic Factor Models in a stationary context, where the latent variables and thus the static and dynamic factors are the sum of a linearly regular and a linearly singular stationary process and the noise process is linearly regular. The linearly singular component may be useful for modeling e.g. business cycles or seasonal fluctuations in the observed variables. We present a structure theory for this case. The emphasis is laid on the autoregressive case. In general the stationary solutions of the autoregressive models considered here consist of a linearly regular and a linearly singular part. The linearly singular part corresponds to the homogeneous solution of a system having stable roots as well as roots of modulus one. We discuss the solutions of the Yule Walker equations for this case