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On the existence of some processes

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  • Douc, Randal
  • Roueff, François
  • Soulier, Philippe

Abstract

A new sufficient condition for the existence of a stationary causal solution of an equation is provided. This condition allows us to consider coefficients with power-law decay, so that it can be applied to the so-called FIGARCH processes, whose existence is thus proved.

Suggested Citation

  • Douc, Randal & Roueff, François & Soulier, Philippe, 2008. "On the existence of some processes," Stochastic Processes and their Applications, Elsevier, vol. 118(5), pages 755-761, May.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:5:p:755-761
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    References listed on IDEAS

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    1. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    2. Basrak, Bojan & Davis, Richard A. & Mikosch, Thomas, 2002. "Regular variation of GARCH processes," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 95-115, May.
    3. Giraitis, Liudas & Surgailis, Donatas, 0. "ARCH-type bilinear models with double long memory," Stochastic Processes and their Applications, Elsevier, vol. 100(1-2), pages 275-300, July.
    4. 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.
    5. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(3), pages 318-334, September.
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    Cited by:

    1. Mawuli Segnon & Rangan Gupta & Keagile Lesame & Mark E. Wohar, 2021. "High-Frequency Volatility Forecasting of US Housing Markets," The Journal of Real Estate Finance and Economics, Springer, vol. 62(2), pages 283-317, February.
    2. Li, Muyi & Li, Wai Keung & Li, Guodong, 2015. "A new hyperbolic GARCH model," Journal of Econometrics, Elsevier, vol. 189(2), pages 428-436.
    3. Davidson, James & Li, Xiaoyu, 2016. "Strict stationarity, persistence and volatility forecasting in ARCH(∞) processes," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 534-547.
    4. HAFNER, Christian & PREMINGER, Arie, 2016. "On Asymptotic Theory for ARCH(infinite) Models," LIDAM Discussion Papers CORE 2016030, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Royer, Julien, 2023. "Conditional asymmetry in Power ARCH(∞) models," Journal of Econometrics, Elsevier, vol. 234(1), pages 178-204.
    6. Christian Francq & Jean-Michel Zakoïan, 2013. "Optimal predictions of powers of conditionally heteroscedastic processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(2), pages 345-367, March.
    7. Royer, Julien, 2021. "Conditional asymmetry in Power ARCH($\infty$) models," MPRA Paper 109118, University Library of Munich, Germany.
    8. Liudas Giraitis & Donatas Surgailis & Andrius Škarnulis, 2015. "Integrated ARCH, FIGARCH and AR Models: Origins of Long Memory," Working Papers 766, Queen Mary University of London, School of Economics and Finance.
    9. Liudas Giraitis & Donatas Surgailis & Andrius Škarnulis, 2015. "Integrated ARCH, FIGARCH and AR Models: Origins of Long Memory," Working Papers 766, Queen Mary University of London, School of Economics and Finance.
    10. Antypas, Antonios & Koundouri, Phoebe & Kourogenis, Nikolaos, 2013. "Aggregational Gaussianity and barely infinite variance in financial returns," Journal of Empirical Finance, Elsevier, vol. 20(C), pages 102-108.
    11. Agnieszka Jach & Piotr Kokoszka, 2010. "Empirical wavelet analysis of tail and memory properties of LARCH and FIGARCH models," Computational Statistics, Springer, vol. 25(1), pages 163-182, March.

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