Asymptotic theory for ARCH-SM models

Lan and residual empirical processes

Sangyeol Lee, Masanobu Taniguchi

    Research output: Contribution to journalArticle

    22 Citations (Scopus)

    Abstract

    In this paper, we have two asymptotic objectives: the LAN and the residual empirical process for a class of ARCH(∞)-SM (stochastic mean) models, which covers finite-order ARCH and GARCH models. First, we establish the LAN for the ARCH(∞)-SM model and, based on it, construct an asymptotically optimal test when the parameter vector contains a nuisance parameter. Also, we discuss asymptotically efficient estimators for unknown parameters when the innovation density is known and when it is unknown. For the residual empirical process, we investigate its asymptotic behavior in ARCH(q)-SM models. We show that, unlike the usual autoregressive model, the limiting distribution in this case depends upon the estimator of the regression parameter as well as those of the ARCH parameters.

    Original languageEnglish
    Pages (from-to)215-234
    Number of pages20
    JournalStatistica Sinica
    Volume15
    Issue number1
    Publication statusPublished - 2005 Jan

    Fingerprint

    Autoregressive Conditional Heteroscedasticity
    Empirical Process
    Asymptotic Theory
    Optimal Test
    GARCH Model
    Efficient Estimator
    Model
    Nuisance Parameter
    Autoregressive Model
    Asymptotically Optimal
    Limiting Distribution
    Unknown Parameters
    Regression
    Asymptotic Behavior
    Empirical process
    Asymptotic theory
    Autoregressive conditional heteroscedasticity
    Cover
    Estimator
    Unknown

    Keywords

    • ARCH model
    • ARCH(∞)-SM model
    • Asymptotically efficient estimator
    • Asymptotically optimal test
    • GARCH model
    • Gaussian process
    • LAN
    • Residual empirical process
    • Weak convergence

    ASJC Scopus subject areas

    • Mathematics(all)
    • Statistics and Probability

    Cite this

    Asymptotic theory for ARCH-SM models : Lan and residual empirical processes. / Lee, Sangyeol; Taniguchi, Masanobu.

    In: Statistica Sinica, Vol. 15, No. 1, 01.2005, p. 215-234.

    Research output: Contribution to journalArticle

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