Spectral Expression of Information Measures for Discrimination and Stochastic Simplification

Abstract

In this paper, we consider the stochastic model simplification (reduction) problem for autoregressive moving average(ARMA) models, with applying the spectral expression of Fisher's information rate matrix. First, we discuss the spectral expression of several information measures for discrimination between two stationary Gaussian time series and show that all of these measures are equivalent and expressed by Fisher's information rate matrix in the sense of their second order Taylor series approximation. Then we propose a criterion for discrimination of two time series so that a new model reduction method for ARMA model is derived in connection with the Levinson-Durbin algorithm and generalized Lyapunov algebraic equations for evaluation of Fisher's information rate matrix. A relation of the present model reduction method for the deterministic system is also discussed.