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

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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.

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Bibliographic Info

Paper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 601.

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Length: 4 pages
Date of creation: 23 Jul 2005
Date of revision:
Handle: RePEc:hhs:hastef:0601

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Keywords: GARCH; strict stationarity; Lyapunov exponent;

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  1. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, Elsevier, vol. 52(1-2), pages 115-127.
  2. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  3. He, Changli & Terasvirta, Timo, 1999. "Properties of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, Elsevier, vol. 92(1), pages 173-192, September.
  4. G. William Schwert, 1990. "Why Does Stock Market Volatility Change Over Time?," NBER Working Papers 2798, National Bureau of Economic Research, Inc.
  5. Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report, Federal Reserve Bank of Minneapolis 157, Federal Reserve Bank of Minneapolis.
  6. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 6(03), pages 318-334, September.
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Cited by:
  1. Marcelo Fernandes & Marcelo Cunha Medeiros & Alvaro Veiga, 2006. "A (semi-)parametric functional coefficient autoregressive conditional duration model," Textos para discussão, Department of Economics PUC-Rio (Brazil) 535, Department of Economics PUC-Rio (Brazil).
  2. Meitz, Mika & Saikkonen, Pentti, 2004. "Ergodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD models," Working Paper Series in Economics and Finance, Stockholm School of Economics 573, Stockholm School of Economics, revised 20 Apr 2007.

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