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A necessary and sufficient condition for the strict stationarity of a family of GARCH processes

Author

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  • Meitz, Mika

    () (Dept. of Economic Statistics, Stockholm School of Economics)

Abstract

We consider a family of GARCH(1,1) processes introduced in He and Teräsvirta (1999a). This family contains various popular GARCH models as special cases. A necessary and sufficient condition for the existence of a strictly stationary solution is given.

Suggested Citation

  • Meitz, Mika, 2005. "A necessary and sufficient condition for the strict stationarity of a family of GARCH processes," SSE/EFI Working Paper Series in Economics and Finance 601, Stockholm School of Economics.
  • Handle: RePEc:hhs:hastef:0601
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    References listed on IDEAS

    as
    1. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, pages 115-127.
    2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, pages 307-327.
    3. Schwert, G William, 1989. " Why Does Stock Market Volatility Change over Time?," Journal of Finance, American Finance Association, vol. 44(5), pages 1115-1153, December.
    4. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    5. He, Changli & Terasvirta, Timo, 1999. "Properties of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, pages 173-192.
    6. He, Changli & Terasvirta, Timo, 1999. "Properties of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, pages 173-192.
    7. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
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    Cited by:

    1. Behar Alberto & Hodge James, 2008. "The Employment Effects of Mergers in a Declining Industry: The Case of South African Gold Mining," The B.E. Journal of Economic Analysis & Policy, De Gruyter, pages 1-20.
    2. Fernandes, Marcelo & Medeiros, Marcelo C. & Veiga, Alvaro, 2013. "A (semi-)parametric functional coefficient autoregressive conditional duration model," Textos para discussão 343, FGV/EESP - Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
    3. Delaigle, Aurore & Meister, Alexander & Rombouts, Jeroen, 2016. "Root-T consistent density estimation in GARCH models," Journal of Econometrics, Elsevier, pages 55-63.
    4. Meitz, Mika & Saikkonen, Pentti, 2008. "Ergodicity, Mixing, And Existence Of Moments Of A Class Of Markov Models With Applications To Garch And Acd Models," Econometric Theory, Cambridge University Press, vol. 24(05), pages 1291-1320, October.
    5. Marcelo Fernandes & Marcelo Cunha Medeiros & Alvaro Veiga, 2006. "A (semi-)parametric functional coefficient autoregressive conditional duration model," Textos para discussão 535, Department of Economics PUC-Rio (Brazil).

    More about this item

    Keywords

    GARCH; strict stationarity; Lyapunov exponent;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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