Maximum likelihood estimation of the autoregressive model by relaxation on the reflection coefficients

A method for autoregressive parameter estimation, which successively maximizes the likelihood with respect to each reflection coefficient while keeping the others fixed, is presented. The algorithm generalizes the recursive-maximum-likelihood technique of S.M. Kay (1983), which corresponds to performing only one iteration cycle. An interesting application is the estimation of a Toeplitz covariance matrix. Simulations show that the algorithm converges quite fast and provides much better estimates than current procedures for short record length