Elsevier

Signal Processing

Volume 32, Issue 3, June 1993, Pages 329-342
Signal Processing

Signal processing
ARMA realization from the reflection coefficient sequence

https://doi.org/10.1016/0165-1684(93)90005-UGet rights and content

Abstract

The problem of ARMA modeling is focused in this paper. It is shown how to compute the ARMA parameters from a finite set of consecutive reflection coefficients in a completely recursive way. The algorithm consists of simple recursions for both the AR and MA parameters and it generalizes in a unifying framework other existing AR and MA algorithms.

Zusammenfassung

Diese Arbeit befaßt sich mit dem Problem der ARMA Modellierung. Es wird gezeigt, wie die ARMA-Parameter aus einer endlichen Menge von Reflexionskoeffizienten in einer vollständig rekursiven Weise berechnet werden können. Der Algorithmus besteht aus einfachen Rekursionen sowohl für die AR als auch die MA Parameter. Er verallgemeinert andere existierende AR und MA Algorithmen zu einem vereinheitlichten System.

Résumé

Le problème de la modélisation ARMA est étudié dans cet article. On montre comment calculer les paramètres ARMA à partir d'un ensemble fini de coefficients de réflexion consécutifs de manière totalement récursive. L'algorithme consiste en des récursions simples à la fois pour les paramètres AR et MA et il généralise dans un cadre unique des algorithmes AR et MA existants.

References (39)

  • M.D. Ortigueira

    A three step algorithm for ARMA modelling

    Signal Processing

    (July 1988)
  • H. Akaike

    A new look at the statistical model identification

    IEEE Trans. Automatic Control

    (December 1974)
  • O.D. Anderson

    A commentary on ‘A Survey of Time Series’

    Internat. Statist. Rev.

    (1977)
  • J.M. Beguin et al.

    Identification of a mixed autoregressive moving average process: The corner method

  • G.E.P. Box et al.

    Time Series Analysis-Forecasting and Control

    (1970)
  • J.P. Burg

    Maximum entropy spectral analysis

  • J.A. Cadzow

    Spectral estimation: An overdetermined rational model equation approach

  • J.A. Cadzow et al.

    Singular value decomposition to time series modelling

  • G. Carayannis et al.

    Fast algorithms for a class of linear equations

    IEEE Trans. Acoust. Speech Signal Process.

    (1982)
  • R.H. Cohen et al.

    New relationships between ARMA and AR processes

  • N. Davies et al.

    On the use of the general partial autocorrelation function for order determination in ARMA (p, q) processes

    J. Amer. Statist. Assoc.

    (June 1984)
  • B.W. Dickinson et al.

    Reflection coefficient estimation using Cholesky decomposition

    IEEE Trans. Acoust. Speech Signal Process.

    (April 1979)
  • V.N. Fadeeva

    Computational Methods of Linear Algebra

    (1959)
  • P.F. Fougere

    A solution to the problem of spontaneous line splitting in maximum entropy power spectrum analysis

    J. Geophys. Res.

    (March 1977)
  • T.T. Georgiou

    Realization of power spectra from partial covariance sequences

    IEEE Trans. Acoust. Speech Signal Process.

    (April 1987)
  • T.T. Georgiou et al.

    Linear fractional transformations and spectral factorization

    IEEE Trans. Automatic Control

    (1986)
  • C.A. Glasbey

    A generalization of partial autocorrelations useful in identifying ARMA models

    Technometrics

    (August 1982)
  • C.W.J. Granger et al.

    Time series modelling and interpretation

    J. Roy. Statist. Soc. A

    (1976)
  • Cited by (0)

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