An efficient method to compute consistent estimates of the AR parameters of an ARMA model

A computationally efficient method for consistent estimation of the AR parameters of an ARMA model is obtained, based on an iterated least squares approach proposed by Tsay and Tiao. The method is derived from the lattice filter structure which generates an orthogonal basis for the Hilbert space of interest. It is shown that for the ARMA(p, q) model, we can get consistent estimates of the AR parameters by using an least squares lattice estimation algorithm and solving a system of q linear equations.