Minimum α-divergence estimation for arch models

S. Ajay Chandra, Masanobu Taniguchi

    Research output: Contribution to journalArticle

    7 Citations (Scopus)

    Abstract

    This paper considers a minimum α-divergence estimation for a class of ARCH(p) models. For these models with unknown volatility parameters, the exact form of the innovation density is supposed to be unknown in detail but is thought to be close to members of some parametric family. To approximate such a density, we first construct an estimator for the unknown volatility parameters using the conditional least squares estimator given by Tjøstheim [Stochastic processes and their applications (1986) Vol. 21, pp. 251-273]. Then, a nonparametric kernel density estimator is constructed for the innovation density based on the estimated residuals. Using techniques of the minimum Hellinger distance estimation for stochastic models and residual empirical process from an ARCH(p) model given by Beran [Annals of Statistics (1977) Vol. 5, pp. 445-463] and Lee and Taniguchi [Statistica Sinica (2005) Vol. 15, pp. 215-234] respectively, it is shown that the proposed estimator is consistent and asymptotically normal. Moreover, a robustness measure for the score of the estimator is introduced. The asymptotic efficiency and robustness of the estimator are illustrated by simulations. The proposed estimator is also applied to daily stock returns of Dell Corporation.

    Original languageEnglish
    Pages (from-to)19-39
    Number of pages21
    JournalJournal of Time Series Analysis
    Volume27
    Issue number1
    DOIs
    Publication statusPublished - 2006 Jan

    Fingerprint

    Autoregressive Conditional Heteroscedasticity
    Arches
    Divergence
    Estimator
    Innovation
    Unknown
    Volatility
    Stochastic models
    Random processes
    Conditional Least Squares
    Hellinger Distance
    Robustness
    Kernel Density Estimator
    Stock Returns
    Statistics
    Asymptotic Efficiency
    Empirical Process
    Least Squares Estimator
    Minimum Distance
    Stochastic Model

    Keywords

    • α-divergence
    • ARCH model
    • Asymptotic efficiency
    • Conditional least squares estimator
    • Kernel density estimator
    • Residual empirical process
    • Robustness

    ASJC Scopus subject areas

    • Applied Mathematics
    • Statistics and Probability

    Cite this

    Minimum α-divergence estimation for arch models. / Chandra, S. Ajay; Taniguchi, Masanobu.

    In: Journal of Time Series Analysis, Vol. 27, No. 1, 01.2006, p. 19-39.

    Research output: Contribution to journalArticle

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