Uniqueness of the maximum likelihood estimates of the parameters of an ARMA model

Kalle Åström, T. Söderström

Type: Article

Publication Date: 1974-12-01

Citations: 202

DOI: https://doi.org/10.1109/tac.1974.1100735

Abstract

Estimation of the parameters in a mixed autoregressive moving average process leads to a nonlinear optimization problem. The negative logarithm of the likelihood function, suitably normalized, converges to a deterministic function as the sample length increases. The local and global extrema of this function are investigated. Conditions for the existence of a unique global and local minimum are given.

Locations

IEEE Transactions on Automatic Control - View
Lund University Publications (Lund University) - View - PDF

Similar Works

Action	Title	Year	Authors
+	Uniqueness of the Maximum Likelihood Estimates of the Parameters of A Mixed Autoregressive Moving Average Process	1973	Karl Johan Åström Torsten Söderström
+	Estimation of ARMA models by maximum likelihood	2008	Jean–Marie Dufour
+	Likelihood Function of Stationary Multiple Autoregressive Moving Average Models	1979	Steven C. Hillmer George C. Tiao
+	An efficient algorithm for calculating the likelihood and likelihood gradient of ARMA models	1993	David Burshtein
+	Likelihood Function of Stationary Multiple Autoregressive Moving Average Models	1979	Steven C. Hillmer George C. Tiao
+	Maximum likelihood estimation for arma models in the presence of ARMA errors	1997	Jong Hyup Lee Dong Wan Shin
+	Conditions for local convergence of maximum likelihood estimation for armax models	2003	Graham C. Goodwin Juan C. Agüero Robert E. Skelton
+	Maximum likelihood estimation for linear regression models with autoregressive errors	1991	Stefan Schäffler
+	The Maximum Likelihood Estimation of Parameters in Mixed Autoregressive Moving-Average Multivariate Models	1977	Rusdu Saracoglu
+	The maximum likelihood estimation of parameters in mixed autoregressive moving-average multivariate models	1977	Rusdu Saracoglu
+	MAXIMUM LIKELIHOOD ESTIMATORS IN THE MULTIVARIATE AUTOREGRESSIVE MOVING‐AVERAGE MODEL FROM A GENERALIZED LEAST SQUARES VIEWPOINT	1992	Gregory C. Reinsel Sabyasachi Basu Sook Fwe Yap
+	Estimation de modèles ARMA par la méthode du maximum de vraisemblance	2002	Jean‐Marie Dufour
+	Maximum Likelihood Estimation using the EM Algorithm	2021	Ahsène Lanani
+	Linear Estimation of ARMA Systems	1978	D.Q. Mayne F. Firoozan
+	On Maximum Likelihood Estimation of Parameters of Autoregressive Moving Average Processes	1977	T. W. Anderson
+	Convergence results for maximum likelihood type estimators in multivariable ARMA models	1987	B.M. Pötscher
+	Maximum likelihood estimation	2019	Jan R. Magnus Jan R. Magnus
+ PDF Chat	Asymptotic Properties of Maximum Likelihood Estimates in the Mixed Model of the Analysis of Variance	1977	J. J. Miller
+ PDF Chat	Multiple Minima in the Estimation of Models with Autoregressive Disturbances	1992	Howard E. Doran Jan Kmenta
+	An Algorithm for the Exact Likelihood of a Mixed Autoregressive-Moving Average Process	1979	Craig F. Ansley

Works That Cite This (32)

Action	Title	Year	Authors
+	On multistep prediction error methods for time series models	1989	Petre Stoica Arye Nehorai
+	A modified Hannan—Rissanen strategy for mixed autoregressive-moving average order determination	1987	D. S. Poskitt
+	Topology of the moduli space for reachable linear dynamical systems: The complex case	1986	Uwe Helmke
+	Uniqueness of Prediction Error Estimates of Multivariable Moving Average Models	1982	Petre Stoica T. Söderström
+	Some Properties of Moving-Average Model Fittings	1992	Minoru Tanaka Mituaki Huzii
+	A Representation Theorem for the Error of Recursive Estimators	2006	László Gerencsér
+	Critical point behavior of objective functions defined on spaces of multivariable systems	1982	David F. Delchamps Christopher I. Byrnes
+	Asymptotic behaviour of some bootstrap estimators	1981	Petre Stoica Torsten Söderström
+	Geometric Aspects of the Convergence Analysis of Identification Algorithms	1983	Christopher I. Byrnes
+	UNIQUENESS OF THE MAXIMUM-LIKELIHOOD ESTIMATES OF THE KALMAN-GAIN MATRIX	1987	Z. Vágó L. Gerencsér

Works Cited by This (1)

Action	Title	Year	Authors
+	Moderne Algebra	1937	B. L. Van der WAERDEN