On Approximate Modeling of Linear Gaussian Processes

The problem we consider here is the elimination of the redundant complexity in the modeling of stationary time series by means of stochastic realization theory. The question is posed in terms of approximate modeling of a gaussian process. It is shown that a minimal representation of the process can be obtained with a very simple algorithm of polynomial complexity from a nonminimal one, and that this algorithm can be extended to give an approximate realization of fixed degree k We also show that different realizations yield different approximation errors, and discuss how to choose the representation which gives the best approximant.