Treffer: An efficient algorithm for calculating the likelihood and likelihood gradient of ARMA models
Title:
An efficient algorithm for calculating the likelihood and likelihood gradient of ARMA models
Authors:
Source:
IEEE transactions on automatic control. 38(2):336-340
Publisher Information:
New York, NY: Institute of Electrical and Electronics Engineers, 1993.
Publication Year:
1993
Physical Description:
print, 10 ref
Original Material:
INIST-CNRS
Subject Terms:
Control theory, operational research, Automatique, recherche opérationnelle, Sciences exactes et technologie, Exact sciences and technology, Sciences appliquees, Applied sciences, Informatique; automatique theorique; systemes, Computer science; control theory; systems, Automatique théorique. Systèmes, Control theory. Systems, Modélisation et identification, Modelling and identification, Algorithme, Algorithm, Algoritmo, Complexité calcul, Computing complexity, Complejidad cálculo, Estimation paramètre, Parameter estimation, Estimación parámetro, Gradient, Gradiente, Maximum vraisemblance, Maximum likelihood, Maxima verosimilitud, Modèle ARMA, ARMA model, Modelo ARMA, Méthode Newton Raphson, Newton Raphson method, Método Newton Raphson, Taux convergence, Convergence rate, Relación convergencia
Document Type:
Fachzeitschrift
Article
File Description:
text
Language:
English
Author Affiliations:
Tel-Aviv univ., dep. electrical eng.-systems, Tel-Aviv 69978, Israel
ISSN:
0018-9286
Rights:
Copyright 1993 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Computer science; theoretical automation; systems
Accession Number:
edscal.4628902
Database:
PASCAL Archive
Weitere Informationen
We obtain exact analytical expressions for the likelihood and likelihood gradient of stationary autoregressive moving average (ARMA) models. Let us denote the sample size by N, the autoregressive order by p, and the moving average order by q. The calculation of the likelihood requires (p+2q+1)N+o(N) multiply-add operations, and the calculation of the likelihood gradient requires (2p+6q+2)N+o(N) multiply-add operations. These expressions may be used to obtain an iterative, Newton-Raphson-type converging algorithm, with superlinear convergence rate, that computes the maximum-likelihood estimator in (2p+6q+2)N+o(N) multiply-add operations per iteration.