System identification with information theoretic criteria

Attention is focused in this paper on the approximation problem of system identification with information theoretic criteria. For a class of problems it is shown that the criterion of mutual information rate is identical to the criterion of exponential-of-quadratic cost and to $H_{infty$ entropy. In addition the relation between the likelihood function and divergence is explored. As a consequence of these relations a parameter estimator is derived by four methods for the approximation of a stationary Gaussian process by the output of a Gaussian system. The unified framework for approximation problems of system identification formulated in this paper seems extremely useful.