  We prove the correspondence between the information geometry of a signal
filter and a K\"ahler manifold. The information geometry of a minimum-phase
linear system with a finite complex cepstrum norm is a K\"ahler manifold. The
square of the complex cepstrum norm of the signal filter corresponds to the
K\"ahler potential. The Hermitian structure of the K\"ahler manifold is
explicitly emergent if and only if the impulse response function of the highest
degree in $z$ is constant in model parameters. The K\"ahlerian information
geometry takes advantage of more efficient calculation steps for the metric
tensor and the Ricci tensor. Moreover, $\alpha$-generalization on the geometric
tensors is linear in $\alpha$. It is also robust to find Bayesian predictive
priors, such as superharmonic priors, because Laplace-Beltrami operators on
K\"ahler manifolds are in much simpler forms than those of the non-K\"ahler
manifolds. Several time series models are studied in the K\"ahlerian
information geometry.
