Notes on poles of autoregressive type model. Part III. General case

Pole locations of a multivariate autoregressive (AR) type model for a Gaussian Markovian process are examined by using the Rouchès theorem. The formalism of the previous papers by the authors (J. Math. Anal. Appl. 124, 1987, 98–116; 123, 1987, 480–493) is generalized. It is shown that when the order of the AR type model becomes large, poles of the AR type model can be classified into three types: (1) poles distributing almost equally spaced on circles which are centered at the origin with radiuses equal to the absolute value of zeros, (2) system poles inside the smallest circle, and (3) robust and non-robust singular poles which were introduced in the papers referenced above.