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On The Tail Behaviors Of A Family Of Garch Processes

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  • Liu, Ji-Chun

Abstract

In this paper, some structural properties of a family of generalized autoregressive conditionally heteroskedastic (GARCH) processes are considered. First, a sufficient and necessary condition for the strict stationarity of this family of GARCH processes is given. Second, some simple conditions for the existence of the moments of the family of GARCH processes are also derived. Finally, we describe the tail of the marginal distribution of the family of GARCH processes.I am grateful to Bruce E. Hansen and an anonymous referee for helpful comments on the initial version.

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  • Liu, Ji-Chun, 2006. "On The Tail Behaviors Of A Family Of Garch Processes," Econometric Theory, Cambridge University Press, vol. 22(5), pages 852-862, October.
    • Handle: RePEc:cup:etheor:v:22:y:2006:i:05:p:852-862_06
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    Cited by:

    1. Haas, Markus, 2008. "The autocorrelation structure of the Markov-switching asymmetric power GARCH process," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1480-1489, September.
    2. Hill, Jonathan B., 2015. "Robust Generalized Empirical Likelihood for heavy tailed autoregressions with conditionally heteroscedastic errors," Journal of Multivariate Analysis, Elsevier, vol. 135(C), pages 131-152.
    3. Choi, M.S. & Park, J.A. & Hwang, S.Y., 2012. "Asymmetric GARCH processes featuring both threshold effect and bilinear structure," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 419-426.

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