Singular arma systems: A structure theory

Singular vector ARMA systems are vector ARMA (VARMA) systems with singular innovation variance or equivalently with singular spectral density of the corresponding VARMA process. Such systems occur in linear dynamic factor models, e.g. if the dimension of the static factors is strictly larger than the dimension of the dynamic factors or in linear dynamic stochastic equilibrium models, if the number of outputs is strictly larger than the number of shocks. We describe the relation of factor models and singular ARMA systems and a realization procedure for singular ARMA systems. Finally we discuss kernel systems.