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 journalJournal articlepeer-review

    5 Citations (Scopus)
    7 Downloads (Pure)

    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 languageEnglish
    Pages (from-to)621-632
    Number of pages12
    JournalStatistical Papers
    Volume52
    Issue number3
    DOIs
    Publication statusPublished - Aug 2011

    Scopus Subject Areas

    • Statistics and Probability
    • Statistics, Probability and Uncertainty

    User-Defined Keywords

    • AR-ARCH model
    • BHHH method
    • Heteroskedasticity
    • Likelihood
    • Newton-Raphson method
    • Scoring method

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