An efficient and order-recursive algorithm for estimating stationary ARMA models

A new Levinson-type recursive algorithm that solves for the coefficients of the pth-order ARMA model using O(p²) operations is proposed. The algorithm uses the fact that in the least squares optimal equation when the system is stationary, the coefficient matrix is "close" to the Toeplitz form. The measures of closeness of a matrix to Toeplitz form is determined by the concept of displacement rank.