We consider the linear Kalman-Bucy filter problem for a system in which a signal and a noise are independent vector stationary autoregressive processes with orders higher than 1. Recurrent equations for the filtration and its error are derived. The optimal definition of the initial data is proposed. We describe an example in which the algorithm leads to a stationary mode at infinity, as well as an example in which the Kalman-Bucy filter is impossible since the filtration error tends to infinity. The behavior of the signal and its filter is illustrated by the simulation of the signal and the noise as Gaussian vector stationary autoregressive processes. These examples support the theoretical conclusions.