A note on recursive maximum likelihood for autoregressive modeling

摘要

Rederives recursive maximum likelihood (RML) for an autoregressive (AR) time series using the Levinson decomposition. This decomposition produces a recursive update of the likelihood function for the AR parameters in terms of the reflection coefficients, prediction error variances, and forward and backward prediction errors. A fast algorithm for this recursive update is presented and compared with the recursive updates of the Burg (1975) algorithm. The comparison clarifies the connection between Burg's algorithm and RML.