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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

Abstract

We consider a family of GARCH(1,1) processes introduced in He and Ter svirta (1999a, Journal of Econometrics 92, 173 192). This family contains various popular generalized autoregressive conditional heteroskedasticity (GARCH) models as special cases. A necessary and sufficient condition for the existence of a strictly stationary solution is given.This research was financially supported by the Jan Wallander s and Tom Hedelius Foundation, Grant J03 41. The author thanks the editor, an anonymous referee, Pentti Saikkonen, and Timo Ter svirta for useful comments.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 22 (2006)
Issue (Month): 05 (October)
Pages: 985-988

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Handle: RePEc:cup:etheor:v:22:y:2006:i:05:p:985-988_06

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  1. G. William Schwert, 1990. "Why Does Stock Market Volatility Change Over Time?," NBER Working Papers 2798, National Bureau of Economic Research, Inc.
  2. 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 157, Federal Reserve Bank of Minneapolis.
  3. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  4. He, Changli & Teräsvirta, Timo, 1997. "Properties of Moments of a Family of GARCH Processes," Working Paper Series in Economics and Finance 198, Stockholm School of Economics.
  5. 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.
  6. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
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Cited by:
  1. Fernandes, Marcelo & Medeiros, Marcelo C. & Veiga, Alvaro, 2013. "A (semi-)parametric functional coefficient autoregressive conditional duration model," Textos para discussão 343, Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
  2. 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.

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