An iterative procedure for moving average models estimation

Using the formulation of Levinson\´s algorithm in terms of cross correlation estimates as presented by RISSANEN, it is shown that, in the case of a finite length autocorrelation serie (i.e. moving average models), this procedure generates a serie that converges towards a causal impulse response . This response has a finite length and its autocorrelation is proportionnal to . Moreover it is shown that has all its roots inside or on the unit cercle (minimal phase response). The proof uses mainly the properties of the PARCOR coefficients.