A note on recursive maximum likelihood for autoregressive modeling

Author

Vis, Marvin L. ; Scharf, Louis L.

Author_Institution

Dept. of Electr. & Comput. Eng., Colorado Univ., Boulder, CO, USA

Volume

42

Issue

10

fYear

1994

fDate

10/1/1994 12:00:00 AM

Firstpage

2881

Lastpage

2883

Abstract

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

Keywords

correlation methods; error analysis; estimation theory; filtering and prediction theory; matrix algebra; maximum likelihood estimation; stochastic processes; time series; Burg´s algorithm; Levinson decomposition; autoregressive modeling; backward prediction errors; fast algorithm; forward and backward prediction errors; prediction error variances; recursive maximum likelihood; reflection coefficients; Covariance matrix; Error correction; Filters; Gaussian noise; Maximum likelihood estimation; Parameter estimation; Probability; Random variables; Reflection; Statistics;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.324761

Filename

324761