A new predictive efficiency criterion for approximate stochastic realization

The problem addressed in this paper is that of realizing a minimum phase ARMA model for a stochastic process, from noisy measurements or estimates of its covariance lags. The new algorithm proposed in this paper optimizes the covariance approximation in terms of the predictive efficiency of the current state vector for the future of the output process. Reasons for preferring the new approximation criterion to canonical correlation analysis are presented, and illustrated with the help of a counter example. Simulations indicate that the new method is capable of high resolution estimates, as compared with existing methods.