On the identification of input-output-noise models

The problem of consistently estimating all parameters of an input-output noise model is considered. It is shown that the parameters of the input-output (deterministic) port of the model may first be estimated consistently when a pure auto-rogressive structure of that part is considered. Subsequently, if a consistent estimation procedure of the noise model is employed, a consistent estimate of the parameters of the complete input-output-noise model is shown to be obtainable.