A NOTE ON RECURSIVE MAXIMUM-LIKELIHOOD FOR AUTOREGRESSIVE MODELING

In this paper, we rederive recursive maximum likelihood (RML) for an a utoregressive (AR) time series using the Levinson decomposition. This decomposition produces a recursive update of the likelihood function f or the AR parameters in terms of the reflection coefficients, predicti on error variances, and forward and backward prediction errors. A fast algorithm for this recursive update is presented and compared with th e recursive updates of the Burg algorithm. The comparison clarifies th e connection between Burg's algorithm and RML.