Hyperbolic decomposition of Dirichlet distance for ARMA models

We investigate the hyperbolic decomposition of the Dirichlet norm and distance between autoregressive moving average (ARMA) models. Beginning with the K\"ahler information geometry of linear systems in the Hardy space and weighted Hardy spaces, we demonstrate that the Dirichlet norm and distance of ARMA models, corresponding to the mutual information between the past and future, are decomposed into functions of the hyperbolic distance between the poles and zeros of the ARMA models.