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The limiting properties of the QMLE in a general class of asymmetric volatility models

Author

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  • Christian M. Dahl
  • Emma M. Iglesias

    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

Abstract

In this paper we analyze the limiting properties of the estimated parameters in a general class of asymmetric volatility models which are closely related to the traditional exponential GARCH model. The new representation has three main advantages over the traditional EGARCH: (1) It allows a much more flexible representation of the conditional variance function. (2) It is possible to provide a complete characterization of the asymptotic distribution of the QML estimator based on the new class of nonlinear volatility models, something which has proven very difficult even for the traditional EGARCH. (3) It can produce asymmetric news impact curves where, contrary to the traditional EGARCH, the resulting variances do not excessively exceed the ones associated with the standard GARCH model, irrespectively of the sign of an impact of moderate size. Furthermore, the new class of models considered can create a wide array of news impact curves which provide the researcher with a richer choice set relative to the traditional. We also show in a Monte Carlo experiment the good finite sample performance of our asymptotic theoretical results and we compare them with those obtained from a parametric and the residual based bootstrap. Finally, we provide an empirical illustration.

Suggested Citation

  • Christian M. Dahl & Emma M. Iglesias, 2008. "The limiting properties of the QMLE in a general class of asymmetric volatility models," CREATES Research Papers 2008-38, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2008-38
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    References listed on IDEAS

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    Cited by:

    1. Sucarrat, Genaro & Escribano, Álvaro, 2009. "Automated financial multi-path GETS modelling," UC3M Working papers. Economics we093620, Universidad Carlos III de Madrid. Departamento de Economía.
    2. repec:imd:wpaper:wp2010-25 is not listed on IDEAS
    3. A. B. M. Rabiul Alam Beg & Sajid Anwar, 2014. "Detecting volatility persistence in GARCH models in the presence of the leverage effect," Quantitative Finance, Taylor & Francis Journals, vol. 14(12), pages 2205-2213, December.
    4. Sucarrat, Genaro & Escribano, Álvaro, 2010. "The power log-GARCH model," UC3M Working papers. Economics we1013, Universidad Carlos III de Madrid. Departamento de Economía.

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    More about this item

    Keywords

    Asymmetric volatility models; Asymmetric news impact curves; Quasi maximum likelihood estimation; Asymptotic Theory; Bootstrap;
    All these keywords.

    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
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

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