An optimal instrumental variable method for ARMA spectral estimation

Author

Zou, Pei Guo ; Du, Lian Shi

Author_Institution

Dept. of Road & Traffic Eng., Tongji Univ., Shanghai, China

Volume

39

Issue

12

fYear

1991

fDate

12/1/1991 12:00:00 AM

Firstpage

2728

Lastpage

2733

Abstract

A multistep iterative and fast recursive algorithm, for autoregressive moving average, (ARMA) spectral estimation is presented. The AR parameters of an ARMA process are estimated using the extended instrumental variable (EIV) method. The optimal choice of instruments, prefilter, and weighting matrix is investigated. A bootstrapping procedure that has computational convenience is proposed for the algorithm. The statistical analysis and experiments show that the optimal IV estimate is unbiased, consistent, efficient, asymptotically normal, and equivalent to the maximum-likelihood (ML) estimate and the prediction error (PE) estimate; and the proposed algorithm has the advantages of sharper resolution, less frequency bias, and better efficiency of convergence

Keywords

iterative methods; parameter estimation; spectral analysis; ARMA spectral estimation; autoregressive moving average; autoregressive parameters; bootstrapping procedure; convergence; extended instrumental variable; fast recursive algorithm; frequency bias; maximum likelihood estimate; multistep iterative algorithm; optimal instrumental variable method; prediction error estimate; prefilter; resolution; statistical analysis; weighting matrix; Algorithm design and analysis; Frequency estimation; Instruments; Iterative algorithms; Lattices; Maximum likelihood estimation; Recursive estimation; Signal processing algorithms; Signal resolution; Statistical analysis;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.107422

Filename

107422