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On asymptotic theory for ARCH([infinite]) models

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  • Christian M. Hafner
  • Arie Preminger

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.
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Suggested Citation

  • Christian M. Hafner & Arie Preminger, 2017. "On asymptotic theory for ARCH([infinite]) models," LIDAM Reprints CORE 2917, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:2917
    Note: In : Journal of Time Series Analysis, 28, 85-879, 2017
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    as
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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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