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.

翻译：本文研究了自回归滑动平均（ARMA）模型间狄利克雷范数与距离的双曲分解。从哈代空间及加权哈代空间中线性系统的凯勒信息几何出发，我们证明了ARMA模型的狄利克雷范数与距离——对应于过去与未来之间的互信息——可分解为ARMA模型极点与零点间双曲距离的函数。