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Renorming Volatilities In A Family Of Garch Models

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  • Li, Dong
  • Wu, Wuqing

Abstract

This paper studies the weak convergence of renorming volatilities in a family of GARCH(1,1) models from a functional point of view. After suitable renormalization, it is shown that the limiting distribution is a geometric Brownian motion when the associated top Lyapunov exponent γ > 0 and is an exponential functional of the maximum process of a Brownian motion when γ = 0. This indicates that the volatility of the GARCH(1,1)-type model has a completely different random structure according to the sign of γ. The obtained results further strengthen our understanding of volatilities in GARCH-type models. Simulation studies are carried out to assess our findings.

Suggested Citation

  • Li, Dong & Wu, Wuqing, 2018. "Renorming Volatilities In A Family Of Garch Models," Econometric Theory, Cambridge University Press, vol. 34(6), pages 1370-1382, December.
    • Handle: RePEc:cup:etheor:v:34:y:2018:i:06:p:1370-1382_00
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    Cited by:

    1. Bonatti, Luigi & Lorenzetti, Lorenza Alexandra, 2023. "Long-term economic implications of Demeny voting: A theoretical analysis," Economic Systems, Elsevier, vol. 47(4).
    2. Eunju Hwang, 2021. "Limit Theory for Stationary Autoregression with Heavy-Tailed Augmented GARCH Innovations," Mathematics, MDPI, vol. 9(8), pages 1-10, April.

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