A note on recursive maximum likelihood for autoregressive modeling - Vis, Marvin L., author; Scharf, Louis L., author; IEEE, publisher (Colorado State University. Libraries, 1994)
In this paper, we rederive 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 algorithm. The comparison clarifies the connection between Burg's algorithm and RML.
Keywords: matrix algebra; maximum likelihood estimation; time series; correlation methods; error analysis; estimation theory; stochastic processes; filtering and prediction theory