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

Shuangzhe Liu; Chris C. Heyde; Wing Keung Wong

doi:10.1007/s00362-009-0272-2

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

Shuangzhe Liu^*, Chris C. Heyde, Wing Keung Wong

^*Corresponding author for this work

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

5 Citations (Scopus)

Abstract

It is well known that moment matrices play a very important rôle 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 language	English
Pages (from-to)	621-632
Number of pages	12
Journal	Statistical Papers
Volume	52
Issue number	3
DOIs	https://doi.org/10.1007/s00362-009-0272-2
Publication status	Published - Aug 2011

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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 r{\^o}le 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.",

keywords = "AR-ARCH model, BHHH method, Heteroskedasticity, Likelihood, Newton-Raphson method, Scoring method",

author = "Shuangzhe Liu and Heyde, {Chris C.} and Wong, {Wing Keung}",

year = "2011",

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doi = "10.1007/s00362-009-0272-2",

language = "English",

volume = "52",

pages = "621--632",

journal = "Statistical Papers",

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

AU - Liu, Shuangzhe

AU - Heyde, Chris C.

AU - Wong, Wing Keung

PY - 2011/8

Y1 - 2011/8

N2 - It is well known that moment matrices play a very important rôle 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 rôle 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 - AR-ARCH model

KW - BHHH method

KW - Heteroskedasticity

KW - Likelihood

KW - Newton-Raphson method

KW - Scoring method

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DO - 10.1007/s00362-009-0272-2

M3 - Article

SN - 0932-5026

VL - 52

SP - 621

EP - 632

JO - Statistical Papers

JF - Statistical Papers

IS - 3

ER -

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

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