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On asymptotic theory for ARCH(infinite) 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.
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Suggested Citation

  • Hafner, Christian & Preminger, Arie, 2017. "On asymptotic theory for ARCH(infinite) models," LIDAM Discussion Papers ISBA 2017009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2017009
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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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    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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