Maximum likelihood estimation of pure GARCH and ARMA-GARCH processes

Christian Francq; Jean Michel Zakoïan

doi:10.3150/bj/1093265632

Maximum likelihood estimation of pure GARCH and ARMA-GARCH processes

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

Abstract

We prove the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator of the parameters of pure generalized autoregressive conditional heteroscedastic (GARCH) processes, and of autoregressive moving-average models with noise sequence driven by a GARCH model. Results are obtained under mild conditions.

Original language	English
Pages (from-to)	605-637
Number of pages	33
Journal	Bernoulli
Volume	10
Issue number	4
DOIs	https://doi.org/10.3150/bj/1093265632
Publication status	Published - 1 Aug 2004
Externally published	Yes

Keywords

ARMA
Asymptotic normality
Consistency
GARCH
Heteroskedastic time series
Maximum likelihood estimation

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10.3150/bj/1093265632

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title = "Maximum likelihood estimation of pure GARCH and ARMA-GARCH processes",

abstract = "We prove the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator of the parameters of pure generalized autoregressive conditional heteroscedastic (GARCH) processes, and of autoregressive moving-average models with noise sequence driven by a GARCH model. Results are obtained under mild conditions.",

keywords = "ARMA, Asymptotic normality, Consistency, GARCH, Heteroskedastic time series, Maximum likelihood estimation",

author = "Christian Francq and Zako{\"i}an, \{Jean Michel\}",

year = "2004",

month = aug,

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doi = "10.3150/bj/1093265632",

language = "English",

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T1 - Maximum likelihood estimation of pure GARCH and ARMA-GARCH processes

AU - Francq, Christian

AU - Zakoïan, Jean Michel

PY - 2004/8/1

Y1 - 2004/8/1

N2 - We prove the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator of the parameters of pure generalized autoregressive conditional heteroscedastic (GARCH) processes, and of autoregressive moving-average models with noise sequence driven by a GARCH model. Results are obtained under mild conditions.

AB - We prove the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator of the parameters of pure generalized autoregressive conditional heteroscedastic (GARCH) processes, and of autoregressive moving-average models with noise sequence driven by a GARCH model. Results are obtained under mild conditions.

KW - ARMA

KW - Asymptotic normality

KW - Consistency

KW - GARCH

KW - Heteroskedastic time series

KW - Maximum likelihood estimation

UR - https://www.scopus.com/pages/publications/33645008897

U2 - 10.3150/bj/1093265632

DO - 10.3150/bj/1093265632

M3 - Article

AN - SCOPUS:33645008897

SN - 1350-7265

VL - 10

SP - 605

EP - 637

JO - Bernoulli

JF - Bernoulli

IS - 4

ER -

Maximum likelihood estimation of pure GARCH and ARMA-GARCH processes

Abstract

Keywords

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