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The Stationary Seasonal Hyperbolic Asymmetric Power ARCH model

Author

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  • Abdou Kâ Diongue

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Dominique Guegan

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

Most financial time series exhibit seasonality, persistence (hyperbolic decay of the autocorrelation function), asymmetric behavior and leptokurtosis. In this paper, we introduce the stationary Seasonal Hyperbolic APARCH model, which can take into account the previous features. We then investigate the probabilistic properties of the process e.g the strict and weak stationarity of the process and the long memory property.

Suggested Citation

  • Abdou Kâ Diongue & Dominique Guegan, 2007. "The Stationary Seasonal Hyperbolic Asymmetric Power ARCH model," Post-Print halshs-00179275, HAL.
    • Handle: RePEc:hal:journl:halshs-00179275
    DOI: 10.1016/j.spl.2007.02.007
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00179275
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    Cited by:

    1. Dark Jonathan Graeme, 2010. "Estimation of Time Varying Skewness and Kurtosis with an Application to Value at Risk," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(2), pages 1-50, March.
    2. Lee, Oesook, 2018. "Stationarity and functional central limit theorem for ARCH(∞) models," Economics Letters, Elsevier, vol. 162(C), pages 107-111.
    3. Conrad, Christian, 2010. "Non-negativity conditions for the hyperbolic GARCH model," Journal of Econometrics, Elsevier, vol. 157(2), pages 441-457, August.
    4. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.

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    Keywords

    Seasonality; Persistence; Asymmetry; Aparch model; Hyperbolic distribution; Stationary solution;
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