Identification of dynamic systems from noisy data: the case m*=n-1

Linear dynamic errors-in-variables (or factor) models in the framework of stationary processes are considered. The noise process is assumed to have a diagonal spectral density. The relation between the (population) second moments of the observations and the system and noise characteristics is analyzed; of particular interest are the number of equations (or the number of factors) and a description of the set of all systems compatible with the second moments of the observations. Emphasis is placed on the case which can be reduced to a single factor. The problems considered arise in the context of identification and precede estimation.<>