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A new fast algorithm for PARCOR parameter estimation based on an approximate likelihood is proposed. The exact likelihood of AR processes based on the Gaussian assumption is approximated by taking the exponential part only. The criterion is just a modification of that of the prewindowed method by using backward predictions. Then, a fast recursive lattice type algorithm is derived. Its performance is compared to those of the Lee-Morf ladder algorithm for the prewindowed method and the covariance ladder algorithm by simulations.