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On the Stationarity of Dynamic Conditional Correlation Models

Author

Listed:
  • Jean-David Fermanian

    () (CREST (ENSAE))

  • Hassan Malongo

    () (Amundi et université Paris-Dauphine)

Abstract

We provide conditions for the existence and the unicity of strictly stationary solutions of the usual Dynamic Conditional Correlation GARCH models (DCC-GARCH). The proof is based on Tweedie's (1988) criteria, after having rewritten DCC-GARCH models as nonlinear Markov chains. Moreover, we study the existence of their finite moments

Suggested Citation

  • Jean-David Fermanian & Hassan Malongo, 2013. "On the Stationarity of Dynamic Conditional Correlation Models," Working Papers 2013-26, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2013-26
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    References listed on IDEAS

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    1. Michael McAleer & Les Oxley, 2011. "Ten Things We Should Know About Time Series," Journal of Economic Surveys, Wiley Blackwell, vol. 25(1), pages 185-188, February.
    2. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(02), pages 280-310, April.
    3. BAUWENS, Luc & otranto, EDOARDO, 2013. "Modeling the dependence of conditional correlations on volatility," CORE Discussion Papers 2013014, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
    5. Gian Piero Aielli, 2013. "Dynamic Conditional Correlation: On Properties and Estimation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 282-299, July.
    6. Lorenzo Cappiello & Robert F. Engle & Kevin Sheppard, 2006. "Asymmetric Dynamics in the Correlations of Global Equity and Bond Returns," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(4), pages 537-572.
    7. Massimiliano Caporin & Michael McAleer, 2013. "Ten Things You Should Know about the Dynamic Conditional Correlation Representation," Econometrics, MDPI, Open Access Journal, vol. 1(1), pages 1-12, June.
    8. Christian Hafner & Philip Hans Franses, 2009. "A Generalized Dynamic Conditional Correlation Model: Simulation and Application to Many Assets," Econometric Reviews, Taylor & Francis Journals, vol. 28(6), pages 612-631.
    9. Maria Kasch & Massimiliano Caporin, 2013. "Volatility Threshold Dynamic Conditional Correlations: An International Analysis," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 11(4), pages 706-742, September.
    10. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    11. Monica Billio & Massimiliano Caporin & Michele Gobbo, 2006. "Flexible Dynamic Conditional Correlation multivariate GARCH models for asset allocation," Applied Financial Economics Letters, Taylor and Francis Journals, vol. 2(2), pages 123-130, March.
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