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Asymmetric GARCH processes featuring both threshold effect and bilinear structure

Author

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  • Choi, M.S.
  • Park, J.A.
  • Hwang, S.Y.

Abstract

A class of asymmetric GARCH models is proposed by combining threshold effect and bilinear structure. The class is referred to as threshold-bilinear GARCH processes. A simulation study demonstrates that the class exhibits diverse asymmetries in volatilities, accommodating existing asymmetric models. Stationarity and existence of moments are discussed. Applications to Korean stock prices are illustrated.

Suggested Citation

  • Choi, M.S. & Park, J.A. & Hwang, S.Y., 2012. "Asymmetric GARCH processes featuring both threshold effect and bilinear structure," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 419-426.
  • Handle: RePEc:eee:stapro:v:82:y:2012:i:3:p:419-426
    DOI: 10.1016/j.spl.2011.11.023
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    References listed on IDEAS

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    1. Hwang, S. Y. & Basawa, I. V., 2004. "Stationarity and moment structure for Box-Cox transformed threshold GARCH(1,1) processes," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 209-220, July.
    2. Liu, Ji-Chun, 2006. "On The Tail Behaviors Of A Family Of Garch Processes," Econometric Theory, Cambridge University Press, vol. 22(05), pages 852-862, October.
    3. Abdou Kâ Diongue & Dominique Guegan & Rodney C. Wolff, 2010. "BL-GARCH model with elliptical distributed innovations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00368340, HAL.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    6. He, Changli & Terasvirta, Timo, 1999. "Properties of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 92(1), pages 173-192, September.
    7. Ling, Shiqing & McAleer, Michael, 2002. "Stationarity and the existence of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 106(1), pages 109-117, January.
    8. Engle, Robert F & Ng, Victor K, 1993. " Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    9. Pan, Jiazhu & Wang, Hui & Tong, Howell, 2008. "Estimation and tests for power-transformed and threshold GARCH models," Journal of Econometrics, Elsevier, vol. 142(1), pages 352-378, January.
    10. Enrique Sentana, 1995. "Quadratic ARCH Models," Review of Economic Studies, Oxford University Press, vol. 62(4), pages 639-661.
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