Identification theory and single realization behaviour

It is customary to use the w.p.l limit and the asymptotic distribution (or asymptotic covariance matrix) as an accuracy measure in system identification. Experiment Design and the choice of estimation techniques may be decided upon, using this covariance expression. If we are going to make just one experiment, we may ask about the rationale for such decisions. How do the properties of my particular data set relate to the (then esoteric and imaginary) asymptotic distribution. In this contribution we discuss how the usual probabilistic environment of the identification problem relates to the single-realization behaviour of the resulting models.