Consistency of global total least squares in stochastic system identification

Global total least squares has been introduced as a method for the identification of deterministic system behaviours. We analyse this method within a stochastic framework, where the observed data are generated by a stationary stochastic process. Conditions are formulated so that the method is consistent in the sense that, when the number of observations tends to infinity, the identified deterministic behaviour converges to the behaviour that provides an optimal appoximation of the data generating process.