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On Asymptotic Theory for ARCH (infinity) Models

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  • Hafner, Christian
  • Preminger, Arie

Abstract

ARCH(infinite) models nest a wide range of ARCH and GARCH models including models with long memory in volatility. The existing literature on such models is quite restrictive in terms of existence of moments. However, the popular FIGARCH, one version of a long memory in volatility model, does not have finite second moments and rarely satisfies the moment conditions of the existing literature. This paper considerably weakens the moment assumptions of a general ARCH(infinite) class of models, and develops the theory for consistency and asymptotic normality of the quasi maximum likelihood estimator.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Hafner, Christian & Preminger, Arie, 2017. "On Asymptotic Theory for ARCH (infinity) Models," LIDAM Reprints ISBA 2017041, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2017041
    Note: In : Journal of Time Series Analysis, vol. 38, p. 865-879 (2017)
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    References listed on IDEAS

    as
    1. Christian Conrad & Berthold R. Haag, 2006. "Inequality Constraints in the Fractionally Integrated GARCH Model," Journal of Financial Econometrics, Oxford University Press, vol. 4(3), pages 413-449.
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    4. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
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    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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