Maximum Likelihood Estimation For Arma Models in the Presence of Arma Errors

Jong Hyup Lee; Dong Wan Shin

doi:10.1080/03610929708831967

Maximum Likelihood Estimation For Arma Models in the Presence of Arma Errors

Jong Hyup Lee, Dong Wan Shin

Department of Statistics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

An ARMA(p, q) process observed with an ARMA(c, d) error has an ARMA (p + c, k) representation with k = max(c + q, p + d) whose parameters satisfy some nonlinear constraints. Identification of the model is discussed. We develop Newton-Raphson estimators for the ARMA(p + c, k) process which take advantage of the information contained in the nonlinear restrictions. Explicit expressions for the derivatives of the restrictions are derived.

Original language	English
Pages (from-to)	1057-1072
Number of pages	16
Journal	Communications in Statistics - Theory and Methods
Volume	26
Issue number	5
DOIs	https://doi.org/10.1080/03610929708831967
State	Published - 1997

Bibliographical note

Funding Information:
This research is supported by a grant from Korea Science and Engineering

Keywords

ARMA error
Identification
Maximum likelihood estimation
Newton-Raphson procedure

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10.1080/03610929708831967

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title = "Maximum Likelihood Estimation For Arma Models in the Presence of Arma Errors",

abstract = "An ARMA(p, q) process observed with an ARMA(c, d) error has an ARMA (p + c, k) representation with k = max(c + q, p + d) whose parameters satisfy some nonlinear constraints. Identification of the model is discussed. We develop Newton-Raphson estimators for the ARMA(p + c, k) process which take advantage of the information contained in the nonlinear restrictions. Explicit expressions for the derivatives of the restrictions are derived.",

keywords = "ARMA error, Identification, Maximum likelihood estimation, Newton-Raphson procedure",

author = "Lee, {Jong Hyup} and Shin, {Dong Wan}",

note = "Funding Information: This research is supported by a grant from Korea Science and Engineering",

year = "1997",

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language = "English",

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journal = "Communications in Statistics - Theory and Methods",

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T1 - Maximum Likelihood Estimation For Arma Models in the Presence of Arma Errors

AU - Lee, Jong Hyup

AU - Shin, Dong Wan

N1 - Funding Information: This research is supported by a grant from Korea Science and Engineering

PY - 1997

Y1 - 1997

N2 - An ARMA(p, q) process observed with an ARMA(c, d) error has an ARMA (p + c, k) representation with k = max(c + q, p + d) whose parameters satisfy some nonlinear constraints. Identification of the model is discussed. We develop Newton-Raphson estimators for the ARMA(p + c, k) process which take advantage of the information contained in the nonlinear restrictions. Explicit expressions for the derivatives of the restrictions are derived.

AB - An ARMA(p, q) process observed with an ARMA(c, d) error has an ARMA (p + c, k) representation with k = max(c + q, p + d) whose parameters satisfy some nonlinear constraints. Identification of the model is discussed. We develop Newton-Raphson estimators for the ARMA(p + c, k) process which take advantage of the information contained in the nonlinear restrictions. Explicit expressions for the derivatives of the restrictions are derived.

KW - ARMA error

KW - Identification

KW - Maximum likelihood estimation

KW - Newton-Raphson procedure

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U2 - 10.1080/03610929708831967

DO - 10.1080/03610929708831967

M3 - Article

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EP - 1072

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

IS - 5

ER -

Maximum Likelihood Estimation For Arma Models in the Presence of Arma Errors

Abstract

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Keywords

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