Moment matrices in conditional heteroskedastic models under elliptical distributions with applications in AR-ARCH models

Shuangzhe Liu, Chris Heyde, Wing-Keung Wong

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Abstract

It is well known that moment matrices play a very important role in econometrics and statistics. Liu and Heyde (Stat Pap 49:455–469, 2008) give exact expressions for two-moment matrices, including the Hessian for ARCH models under elliptical distributions. In this paper, we extend the theory by establishing two additional moment matrices for conditional heteroskedastic models under elliptical distributions. The moment matrices established in this paper implement the maximum likelihood estimation by some estimation algorithms like the scoring method. We illustrate the applicability of the additional moment matrices established in this paper by applying them to establish an AR-ARCH model under an elliptical distribution
Original languageEnglish
Pages (from-to)621-632
Number of pages12
JournalStatistical Papers
Volume52
Issue number3
DOIs
Publication statusPublished - 2011

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Autoregressive Conditional Heteroscedasticity
AR Model
Moment Matrix
Elliptical Distribution
Conditional Model
Estimation Algorithms
Econometrics
Scoring
Maximum Likelihood Estimation
Autoregressive conditional heteroscedasticity
Conditional model
Elliptical distribution
Statistics

Cite this

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title = "Moment matrices in conditional heteroskedastic models under elliptical distributions with applications in AR-ARCH models",
abstract = "It is well known that moment matrices play a very important role in econometrics and statistics. Liu and Heyde (Stat Pap 49:455–469, 2008) give exact expressions for two-moment matrices, including the Hessian for ARCH models under elliptical distributions. In this paper, we extend the theory by establishing two additional moment matrices for conditional heteroskedastic models under elliptical distributions. The moment matrices established in this paper implement the maximum likelihood estimation by some estimation algorithms like the scoring method. We illustrate the applicability of the additional moment matrices established in this paper by applying them to establish an AR-ARCH model under an elliptical distribution",
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Moment matrices in conditional heteroskedastic models under elliptical distributions with applications in AR-ARCH models. / Liu, Shuangzhe; Heyde, Chris; Wong, Wing-Keung.

In: Statistical Papers, Vol. 52, No. 3, 2011, p. 621-632.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Moment matrices in conditional heteroskedastic models under elliptical distributions with applications in AR-ARCH models

AU - Liu, Shuangzhe

AU - Heyde, Chris

AU - Wong, Wing-Keung

PY - 2011

Y1 - 2011

N2 - It is well known that moment matrices play a very important role in econometrics and statistics. Liu and Heyde (Stat Pap 49:455–469, 2008) give exact expressions for two-moment matrices, including the Hessian for ARCH models under elliptical distributions. In this paper, we extend the theory by establishing two additional moment matrices for conditional heteroskedastic models under elliptical distributions. The moment matrices established in this paper implement the maximum likelihood estimation by some estimation algorithms like the scoring method. We illustrate the applicability of the additional moment matrices established in this paper by applying them to establish an AR-ARCH model under an elliptical distribution

AB - It is well known that moment matrices play a very important role in econometrics and statistics. Liu and Heyde (Stat Pap 49:455–469, 2008) give exact expressions for two-moment matrices, including the Hessian for ARCH models under elliptical distributions. In this paper, we extend the theory by establishing two additional moment matrices for conditional heteroskedastic models under elliptical distributions. The moment matrices established in this paper implement the maximum likelihood estimation by some estimation algorithms like the scoring method. We illustrate the applicability of the additional moment matrices established in this paper by applying them to establish an AR-ARCH model under an elliptical distribution

KW - Heteroskedasticity

KW - Likelihood

KW - AR-ARCH model

U2 - 10.1007/s00362-009-0272-2

DO - 10.1007/s00362-009-0272-2

M3 - Article

VL - 52

SP - 621

EP - 632

JO - Statistische Hefte

JF - Statistische Hefte

SN - 1613-9798

IS - 3

ER -