Finite sample properties of system identification methods

In this note, we study the quality of system identification models obtained using the standard quadratic prediction error criterion for a general linear model class. The main feature of our results is that they hold true for a finite data sample and they are not asymptotic. The main theorems bound the difference between the expected value of the identification criterion evaluated at the estimated parameters and at the optimal parameters. The bound depends naturally on the model and system order, the pole locations, and the noise variance, and it shows that although these variables often do not enter in asymptotic convergence results, they do play an important role when the data sample is finite.