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Regular Variation of Popular GARCH Processes Allowing for Distributional Asymmetry

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Abstract

Linear GARCH(1,1) and threshold GARCH(1,1) processes are established as regularly varying, meaning their heavy tails are Pareto like, under conditions that allow the innovations from the, respective, processes to be skewed. Skewness is considered a stylized fact for many financial returns assumed to follow GARCH-type processes. The result in this note aids in establishing the asymptotic properties of certain GARCH estimators proposed in the literature.

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  • Todd Prono, 2017. "Regular Variation of Popular GARCH Processes Allowing for Distributional Asymmetry," Finance and Economics Discussion Series 2017-095, Board of Governors of the Federal Reserve System (U.S.).
    • Handle: RePEc:fip:fedgfe:2017-95
    DOI: 10.17016/FEDS.2017.095
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    References listed on IDEAS

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    6. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
    7. Igor Vaynman & Brendan K. Beare, 2014. "Stable Limit Theory for the Variance Targeting Estimator," Advances in Econometrics, in: Essays in Honor of Peter C. B. Phillips, volume 33, pages 639-672, Emerald Group Publishing Limited.
    8. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(1), pages 17-39, February.
    9. Basrak, Bojan & Davis, Richard A. & Mikosch, Thomas, 2002. "Regular variation of GARCH processes," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 95-115, May.
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    11. Todd Prono, 2016. "Closed-Form Estimation of Finite-Order ARCH Models: Asymptotic Theory and Finite-Sample Performance," Finance and Economics Discussion Series 2016-083, Board of Governors of the Federal Reserve System (U.S.).
    12. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-596, May.
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    More about this item

    Keywords

    GARCH; Pareto tails; Heavy tail; Regular variation; Threshold GARCH;
    All these keywords.

    JEL classification:

    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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